1 Kalay University Research Journal Edible Algae from Kalay and its Surrounding Area Moat War Dine Naw 1 and Thein 2 Abstract Algae are useful not only for producing medicine, but also for manufacturing fertilizer and other products. Some algae are edible. This study focuses on the algae, which can be used as human food. In this paper four genera of edible algae were described with photographs. The uses of these algae also mentioned. Introduction Algae are a "group of plants" that dominates the aquatic environment. The macroalgae, usually to as seaweed, have been commercially cultured for over (300) years. Historically, records have established that people collected seaweed for food since (2500) years ago in China (Tseng, 1981). European people collected seaweeds for (500) years. Of these macroalgae, the most widely consumed throughout the world is the red alga Porpyra, called "nori" in Japan and "purple laver" in the west. There are three major commerical groups of phyco colloids; agar-agar, algins and caregeenans produced from macroalgae. Microalge are generally referred to as organisms that are less than 2mm. Today, microalgae are cultivated directed for foods or other products. The history of cultivation of these microscopic plants date back to the Aztecs. The most important microalgeae under modern cultivation are Spirulina, Chlorella, Dunaliella, Haematococcus, Scenedesmus etc (Pulz, 2001). These algae are grown for several puposes; foods, medicines, feeds and chemical compounds. Historically, both macroalgae and microalgae have been collected from the wild fresh water and marine. The seaweed resource of Myanmar was reported by Soe Tun in 1998. Inland algae occurred abundantly in fresh water environments. Some fresh water algae are used as food in upper Myanmar. However, there is no record of beneficial algae from Kalay regions. To fulfill this gap, this study emphasized on edible algae which are found in Kalay and its surrounding area. In this paper four genera of edible algae are mentioned with their description, photographs and uses in other regions. The aim of this study is to contribute some information about economic importance of algae. 1 Assistant lecturer, Department of Botany, Kalay University 2 Demonstrator, Department of Botany, Kalay University
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1
Kalay University Research Journal
Edible Algae from Kalay and its Surrounding Area
Moat War Dine Naw 1and Thein
2
Abstract
Algae are useful not only for producing medicine, but also for
manufacturing fertilizer and other products. Some algae are edible. This
study focuses on the algae, which can be used as human food. In this paper
four genera of edible algae were described with photographs. The uses of
these algae also mentioned.
Introduction
Algae are a "group of plants" that dominates the aquatic environment.
The macroalgae, usually to as seaweed, have been commercially cultured for
over (300) years. Historically, records have established that people collected
seaweed for food since (2500) years ago in China (Tseng, 1981). European
people collected seaweeds for (500) years. Of these macroalgae, the most
widely consumed throughout the world is the red alga Porpyra, called "nori"
in Japan and "purple laver" in the west. There are three major commerical
groups of phyco colloids; agar-agar, algins and caregeenans produced from
macroalgae.
Microalge are generally referred to as organisms that are less than
2mm. Today, microalgae are cultivated directed for foods or other products.
The history of cultivation of these microscopic plants date back to the Aztecs.
The most important microalgeae under modern cultivation are Spirulina,
Chlorella, Dunaliella, Haematococcus, Scenedesmus etc (Pulz, 2001). These
algae are grown for several puposes; foods, medicines, feeds and chemical
compounds.
Historically, both macroalgae and microalgae have been collected from
the wild fresh water and marine. The seaweed resource of Myanmar was
reported by Soe Tun in 1998. Inland algae occurred abundantly in fresh water
environments. Some fresh water algae are used as food in upper Myanmar.
However, there is no record of beneficial algae from Kalay regions. To fulfill
this gap, this study emphasized on edible algae which are found in Kalay and
its surrounding area. In this paper four genera of edible algae are mentioned
with their description, photographs and uses in other regions.
The aim of this study is to contribute some information about
economic importance of algae.
1 Assistant lecturer, Department of Botany, Kalay University
2 Demonstrator, Department of Botany, Kalay University
2
Kalay University Research Journal
Material and methods
Algae are collected from several spring, streams and river, especially
from Kyawk tha lone chaung and Zi chaung in Kalay and its surrounding area.
Results
Edible Algae Cladopora, Spirogyra, Nostoc and Nostochopsis were
abundantly occur this areas during October to February.
1. Cladophora Kuetzing
Division - Chlorophyta
Class - Chlorophyceae
Order - Cladophorales
Family - Cladophoraceae
Collection - Kyawk tha lone chaung and zi chaung
Deseripton : A repeatedly-branched filamentous thallus with basal-
distal differentiation; attached when young but in some species becoming free-
floating; forming feathery tufts on substances, especially in flowing water;
branching alternate, opposite, or sometimes di-or trichotomous, the branches
smaller than the main axis, or at least tapering slightly toward the apices; cells
cylindrical or swollen; walls thick and lamellate in most species, sometimes
thin and firm; chloroplast a parietal reticulum which sometimes becomes
fragmented and appears as numerous discs; pyrenoids present; asexual
reproduction by zoospores; sexual reproduction by isogametes produced in
apical or subapical, unspecialized cells.
Uses: Cladophora is steamed for food in Kachin State and many regions.
But in Taunggyi and Kalay-tung regions, Cladophora is made as algal sheet
and dried to eat.
2. Spirogyra Link
Division - Chlorophyta
Class - Chlorophyceae
Order - Zygnematales
Family - Zygnemataceae
Collection - Small spring near the Zalatni Hostel
Description: Filaments long at and unbranched, usually without basal-distal
differentiation but sometimes with rhizoidal branches developing laterally
where the filament comes in contact with substrate. Cells cylindrical, short
replicate, or colligate (exterior H-shaped piece) end walls. Chloroplast a
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Kalay University Research Journal 2010
parietal band or ribbon which may be spirally twisted 1/2 or 3 (rarely 8) turns,
or may be nearly straight, 1-16 chloroplasts in a cell. Conjugation either lateral
or scalariform, usually by the formation of tubes, rarely by geniculation
bending of the filament so that conjugating cells are brought into juxapositon.
Zygospores formed in one of gametangial cells, which may become swollen,
depending upon the species; zygospores ovate, subglobose, ellipsoid, or
oblong, with 3-layered walled, of which the middle layer may be smooth or
decorated and colored.
Spirogyhra is the largest genus in number of species and the most
common of Zygnemataceae. It is identifiable in the field by its bright green,
cottony growths and its slippery mucilaginous texture. In hand, a mass of
filaments is easily drawn out into a long fine thread. In deep cold spring and
pools Spirogyra flourishes abundantly and vegetative, forming enormous
green 'clouds' several feet in diameter in favorable habitats. In shallow warm
water it has a tendency to form floating mats, with conjugation and subsequent
disintegration of the filaments occurring. During conjugation the plant masses
becomes dull, dirty-green or brownish.
Uses: Spirogyra is use as food in India and Indochina. In Myanmar,
especially in Shan state, fresh and dried. Spirogyra is used in soup as
ingredient.
3. Nostoc Vaucher
Division - Cyanophyta
Class - Cyanophyceae
Order - Nostocales
Family - Nostocaceae
Collection - Kalay University Campus.
Description: Membranous or globular or irregularly lobed colony of tangled,
uniseriate unbranched trichomes of globose and bead-like, barrel-shaped, or
cylindrical cells, inclosed in copious, thick mucilage which outwardly forms a
firm integument, giving the colony a fixed and definite shape; individual
sheaths of the trichome confluent with the colonial mucilage; trichomes
without basal-distal differentiation, made up of vegetative cells, frequent
heterocysts and, when mature, gonidia which are either solitary or in series.
Uses: N.commune is collected in moist hilly locations in the Philippines and
eaten as green salad. Some other Nostoc spp. is also collected in the same area.
In Thailand N. verrucosum is used for food. The marine form of N.commune
is collected for food in China, Japan and Java (Indonesia). The dried algae are
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Kalay University Research Journal
cooked with noodles, vegetables and mushrooms and served as a vegetarian
dish or a soup by Chinese. They often serve it as New Year's dish.
Certain species of Nostoc algae are eaten in Japan (so-called Suizenji-
nori, Jusentai, and Kawatake-nori, products of nothern Kyushu). Today these
species are cultivated only on the gravel-covered bottoms of small, flowing,
clear rivers near the city of Amagi, in Fukuoka Prefecture. Some species grow
near grass roots and flourish throughout the year as perennials. They grow in
riverbeds or in marshes. But today both the algae and the custom of eating
them have died out. A Nostoc growing in fields with pork and is eaten in
Okinawa. This variety has high vitamin B1 content.
In Myanmar N. muscorum and N. commune are used as vegetable food
and traditional medicine. Consumptions of N. muscorum is known to have
been made to overcome the iodine deficiency, especially in mountain regions,
from ancient time. In Taunggyi, Loikaw, Kyaukme, Pyin-Oo-Lwin, they are
used as health-promoting food for iodine deficiency, and remedy for weakness
in chronic invalids and persons of general illness. In Magway, Mon-ywa,
Myo-tha, Shwe-bo, Kyaukse and Mandalay, Nostoc species are used for food
after boiling. It is also used as salad mixed with lemon Juice, chopped green
chili, vermicelli, meat and a pinch of salt. In some Chinese curry Nostoc
(Kyauk-pwint in Myanmar) is cooked with chicken, fish or pork. Nostoc used
in pork or chicken soup enchances its flavor and taste.
4. Nostochopsis Wood em. Geitler
Division - Cyanophyta
Class - Cyanophyceae
Order - Nostocales
Family - Nostocaceae
Collection - Small spring in Tidem Township
Description: Thallus attaches at first, later free-floating with erect filaments
with soft diffluent sheath, mucilaginous, more or less hemispherical, at first
solid, later hollow, torn and expanded; trichome a single or two rows of
branches, branches of two types, one long and many celled, the other one of
limited growth with a heterocyst at the end (pedicellate heterocysts), pedicels
made of one of three cells; heterocysts intercalarys or terminal or pedicellate
or lateral and sessile; hormogones present; spores not known.
Uses: Local people of Mawlu, Indaw called it "Kyauk pwint". The way of
eating is same as Chaetophora.
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Kalay University Research Journal 2010
Cladophora
Spirogyra
Cladophora, dried sheet
Spirogyra, collection
Nostochopsis Nostoc
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Kalay University Research Journal
Table . 1 Differential characters of four collective edible Algae
Than Than Oo, 2006. Economic Geology of the Chromitites of the Tagaung Taung Area,
Thabeikkyin Township, Mandalay Division, Ph. D. Thesis, Y. U., unpub.
Thura Oo, 1993. Geology of the Thaungpwet Taung Area in Thabeikkyin, Momeik Township,
M. Sc Thesis, M. U., unpub.
Tucker, M.E., 2001. Sedimentary Petrology, 3rd
Edition, Blackwell Science Ltd.
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Kalay University Research Journal
Administrative Service Women in Bagan Society
Tin Maung Htwe*
Abstract
The first Myanmar Empire came into existence with Bagan city as
its capital during the 11th
Century AD. The Bagan administration can be
studied in three different branches; civil administration, local administration
and general administration. Women in the Bagan period were found not to
inferior to men in the administrative sectors.
Key word: Bagan society, Women, Civil Administration, Local
Administration, General Administration.
The first Myanmar Empire came into existence with Bagan city
as its capital (administrative centre or political centre) during the 11th
Century
AD. Myanmar chronicles claim that a king known as Samuddaraj, organizing,
19 disintegrated villages in AD 667, founded a city at a place, called
Yonhlukyun and started the Bagan dynasty1. On the basis of historical
evidences, Dr. Than Tun suggested that, before 11th
Century AD, there were
region wise rulers, or Man22
(kings). But the city then was only at the level of
Kharuin and tuik (Division). In the 11th
Century AD., Myanmar people,
centering Bagan as the seat of administration, occupied the surrounding
regions, established a "nui³³am"(country) thus in history, the First Myanmar
nui³³am emerged. The first king of First Myanmar was its founder Aniruddha(AD 1044-1077) and Bagan, the capital, was the centre of administration3. The name "Bagan"4 was first seen in Myanmar language in AD 1196. In stone inscription, Bagan is used to be inscribed as "Arimaddhanapþra", meaning the capital crushing its enemies. Shya³
Disæpræmuk who went to China in AD 1285, referred to Bagan as 'Tampratik',
meaning Copper Country5.
According to evidence of inscription, the boundary of Bagan expended
by Aniruddha and the successive kings was Konican6 from the north to
* Assistant Lecturer, Department of History, University of Kalay 1 Hunanan Yazawintawgyi (Glass Palace Chronicle) Vol. I, Yangon, New light of
Myanmar in Guardian Press, 1992, pp. 186-187. 2 PL 143/a
16 (143/a
16 means Plate No. 143/a in Five Portfolios of Inscriptions of Burma,
line 16) 3 Than Tun, Dr. Khithaungyazawin (The Old History of Myanmar) Yangon, Mahadagon
Press 1969, p. 118(Henceforth Than Tun, 1969). 4 In Old Mon, Pukam is witten Pokam and Possibly Bukam. Bagan in Myanmar is correct
rendering of Pukam 5 Luce Luce, G.H, "Note of the peoples of Burma in the 12
th – 13
th Century AD", JBRS,
XLII, i, 1959, P. 37, 39. 6 Konican was on the left bank of the river, near the later Kaungton, (Luce, G.H,
"Grography of Burma under the Pagan Dynasty", JBRS, XLII, i, 1959, p. 49 (Henceforth
Luce 1959).
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Kalay University Research Journal 2010
tolui³sare and Tawai1 to the south
2. In accordance with the inscription of AD
1196, the territory of Bagan Kingdom during the reign of the Cañsþ II (AD
1174-1211) was Takon and Næchonkhyam3 in the north; Sala³kre in the sourth, Macchakiri (Chin Hills) in the west and the Salwan in the east4. Dr.Than Tun remarked, with regard to the boundary of Bagan, that if wherever votive tablets containing the Aniruddha stamp was found was considered as Aniruddha's authority – extended area, it could be said that Momeik from the north to Tainatharyi coastal region to the south included in the boundary of the Bagan Kingdom5. Under absolute monarchical system, the king was the most important person in a country. But an administrative machinery could not be carried out be a king single – handedly. As the state became wider, officials had to be appointed to assist the king.
The Bagan administration can be studied in three different branches; civil administration, local administration and general administration. Women in the Bagan period were found not to be inferior to men in the administrative sectors. The study of inscriptions show that hierarchy of official positions below ma³krø (rifBuD), the king, were amatyæ6(trmus)( or) amat (trwf)(The
king's counselors of high officials of the Myanmar royal court), sampya³7(oHysif) and kalan8 (uvef) (high servicemen to the crown9). In
inscriptions of later Bagan period, sampya³ and amat were found to be used as equal official ranks10. Kalan, howere, seemed to be inferior to sampya³ in rank. 'Sampya³' was defined as official administering a number of villages11 and as the term denoting from Mahasenapati – Army General, to king's counselors and officials12.
Apart from them, there were many servicemen inside the court. They were (udkifrI) kuiwmhu13 who were likely to be referred to officers commanding
bodyguards who were responsible for the king's security at the palace, 1 Tainatharyi coastal region.
2 PL 276/a
2
3 Nachonkhyam was on the site of modern Bhamo. (Luce 1959, p. 50)
4 Pl 19/a
5 Than Tun, Dr. Athimyin Bamathamaing(New Outlook on Myanmar History), Mandalay,
Thukhawadi Press, 1975, pp.503-504. 6 PL 96
6, PL 194
3
7 PL 24
5, PL 78
10
8 PL 11
6, PL 89
3
9 Khin Khin Sein, Daw,"Bagankhit Amyothamimyar(Women in Bagan Period)" Research
in Burmese History No.1, Yangon, Sarpay Beikman Press, 1977, p. 6 (Henceforth Khin
Khin Sein, 1977) 10
Than Tun, 1969, p. 142. 11
(a) Pe Maung Tin, U. Some Old Words in the Inscription, JBRS, XX, i, 1930, p. 20.
(b) Myanmar Abidanakyinchoke (Outline of Myanmar Dictionary), Vol. V, Yangon,
Sarpay Beikman Press, 1980, p. 203. 12
Than Shwe, Daw. Myanmar Bartharsakar, Myanmar Kyauksar Sarthan Saungparmyar
(Myanmar Language, Articles from Myanmar Stone Inscriptions), Yangon, Department
of Higher Education, 1980 13
Than Tun, 1969, p. 142.
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Kalay University Research Journal
ma³khya³1 (rifcsif) who were companions of the king, ma³ciy2 (rifpd,f) who
were servants of the king, ma³lua³3 (rifvkvif) who were yong men had to
always attend on the king and royal princes concerned. They could be assumed to serving as the present – day personal assistants and secretaries4. Besides there were also su³ait (sþ³ayto)5 (oli,fwyf). Sþ³ayto seemed to be
the kings favorites who grew up with him6. Moreover there were also Atwa³ruy7 (twGiff½k,f), cæmro³8 (pmajrmif) cækhyøpiuw9 (pmcdydkpf) cækhø10 (pmcD) at
at the royal court. It seems they had to note and write down the king's orders and had to send them to those concerned. Mra³ ci (jrifpD), horsemen, controlled
by mra³sþkrø (jrifolBuD;), leder of horsemen, were charged with the duty of
sending the king's to distant territories11.
Apart from the alearly mentioned service men relating to civil administration, there were also servicemen relating to local administration. In that period, for the security of the northern part of the country, there was separate Northern Administrative Headquarters. The official incharge of that Headquarters was called Ko³ca³ Mahæsaman12. His official position seemed to be equal to the present-day post of the Governor ruling a state; and in the provincial administration he might be highest official. The remaining administrative servicemen were kliy sþkrø13 (ud’,folBuD;) to administer the
remote areas of the capital; tuiksþkrø14 (wkdufolBuD) to rule the areas included in
the boundary of tuik, mruiw sþkrø15 (NrdifolBuD) to rule a town (or) fortress16, rwæ
sþkrø17 (&GmolBuD) to rule villages18, and like rwæ sþkrø, there were other sþkrø19
who had to take responsibility of managing and carrying out administrative and social affairs in villages. Of the above mentioned administrative service personnel, the post of kily sþkrø and muri sþkrø were held by the royal relative and queens20. It may, therefore, be expected that those posts in the civil
1 PL 257
13, PL 268
10-11
2 PL 215/b
6-7
3 PL 290/b
3
4 Khin Khin Sein, 1977, p.6.
5 PL 272
19
6 Than Tun, 1969, p. 143.
7 PL 207
13,16
8 PL 235
45
9 PL 232
2, 18
10 PL 268
13
11 Than Tun, 1969, pp. 159-160.
12 PL 258
13 PL 196
5
14 PL 12
5
15 PL 370
23 , PL 392
16
16 Khin Khin Sein, Daw, Bagan Khit Yinkyaehmu (The Civilization of Bagan), Yangon
administration would be high-ranking ones. But they would be inferior to the post of mahæsaman. The post of sþkrø relating to village and the remaining posts might be guessed as inferior ranks.
In the general administration sector, there were also separate crown
service men who were vitally important as they were charged with the duty of
collecting customs and revenue and managing the customs and revenues so
collected. Of them, kumtham (ukHxrf) and bhumma (bkr®) were servicemen
responsible for collecting various taxes and revenues, according to royal orders1. Kø sþkrø 2(uDolBuD;), headman of granary, and kø sañ (uDonf) and kø
co³3(uDapmif) under his supervision were those responsible for looking after
and safeguarding the Royal Granary where paddy and rice offered by people were stored.
From the above-mentioned facts, it is learnt that, among those who
assisted the king in his executive affairs, the amattræ (or) amat, high official of
the royal court, was the highest in rank. Amat meant an advisor to the king4. In
In Myanmar royal court, there were not only man amat, but also woman amat.
In an inscription in inscribed in AD 1209, which lay inside the wall of the Lay
Myet Hna Pagoda of Bagan, the name of a woman amat, high officials, was
found as follows: -"ma³ mat Nagapuir Mi Phawæ5 ". It can be inferred that Mi
Mi Phwæ, was an amat, holding Nagapuir village in fief.
Again in the Theindaw Pagoda inscription inscribed in AD 1231 was
seen "ma³ (a) matyæ Acalapijañ si purhæ a thþ so"6. Donated to the pagoda by
by amat Acalapijan. It is also discovered that the woman amat in this case was the "Acalapijañ" meant a person who tired to free him or herself from being obsessed by agadilepæ , bias of four kinds, namely doing wrong because of love, doing wrong because of anger, doing wrong because of fear, and doing wrong because of ignorance; and who could carry out a task steadfastly to achieve success7. Such a qualified woman amat would have been a distinguished person in the administrative system of Bagan. As an amat was the highest official in rank below the king, the amat (s) were the most influential and powerful crown service personal. Therefore those woman amat would have been influential over various grades of service men, and would have won respect of people.
1 Khin Khin Sein, 1986, p. 44.
2 PL 162
25
3 PL 40
18, PL 148 /b
3
4 Myanmar Abidanakyinchoke (Outline of Myanmar Dictionary), Vol. IV, Yangon, Sarpay
Beikman Press, 1980, p. 102. 5 PL 84
3
6 PL 134/a
2-3
7 Than Shwe, 1980, p. 67.
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Kalay University Research Journal
Below amat in the hierarchy of administration were 'sampya³ and
'kalan'. In the study of inscriptions made so far, no woman sampya³ has ever
been found. This might be because the duties of a sampya³ included military
service, which was appropriate for men only; and women were thus probably,
by their nature, not given these post.
Evidences of inscriptions inscribed during the Bagan period, however,
show that there had been women serving in the kalan post in that period. The
description, "kalæ³ Ai, Phuh Ton1" was found in the Acolat inscription dated
AD 1165; the word, "Kha³ Pa kalan"2 was found in an inscription inscribed in
AD 1224; and in an inscription, the word, 'Apwækala³sikha³ '3 was
discovered. It is on the basis of these evidences that it can be firmly said that
there had been woman as kalans in the Bagan period. Accordingly, in that
period, qualified women had been exalted by being conferred upon higher
posts, and they took part in the administrative sector actively like men.
No service women were found in security and military service sectors
requiring martial prowess. However there were service women in the crown
service units, such as royal script writers, amhætore, amanuensis of the royal
court, atwa³re, secretary, cæmro³, cækhøpuil and cækhø all clerical staff who needed to be qualified educationally.
At this juncture, the term "atwa³uy " (atwa³re), might be regarded as referring to a trusted person (confidant) who had to discharge the king's service in the court. In an inscription inscribed in AD 1311, the name of a woman atwa³re, confidant was found as a proof of donation of slaves, like this, "Ui Lac Cway San, atwa³re"4. From this inscriptions, it is learnt that there there were women atwa³re, trusted persons, who were literates. " Caw Rahan Sima inscription", dated AD 1212, in which described "Ui Pan U Sa³ cækhøpil "5 and the "Bhui Kalun Gubhuræ " hollow Pagoda (or) Ma Rhak Sañ Gubhuræ inscription inscribed in AD 1243, which mentioned, "sakha³ cætawkhø Ui Khi Rhæ Sa³ "6 it is learnt that there had been woman cækhøpuil and cætawkhø, clerks. The group of words, "ma³myæ cæhøpuir" 7of an inscription in AD 1271 shows that a concubine of King Narathihapate (AD 1254-87) had served as cækhøpuil. It is learnt, therefore, from such studies, that during the Bagan period, maids of honour of lesser – queen who were addressed as sakha³ in honour had served as 'cækhøpuil ' and cætawkhø , clerical staff.
1 PL 4
5
2 PL 53
15
3 PL 199
2,3,10
4 PL 207
13
5 PL 36
2
6 PL 150
10
7 PL 232
2
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Kalay University Research Journal 2010
Apart from these service women in civil administration, there were also women serving as kliy sþ krø, in the remote areas of the capital; 'mrui sþkrø ruling a town, and rwæ sþkrø responsible for village administration. The
words, "amipurhæc le kliy sþkri phlac rakæ 1", found in Maharac ceti
inscription, inscribed in AD 1260 shows that the post of kliy sþkrø was
assigned to a queen. From such descriptions as "sukrø I Cwæy Sa³2 " found in
the "sa³lya³ Ui Kap Sa³ Khya³ " inscription, inscribed in AD 1213, and "rwæ
sþkriy May E3" found in an inscription dated AD 1217. It can be learnt that
there had been woman sþkrø who were regarded to take responsibility of and
supervising administrative and social affairs in a ward of village.
There had also been female "kyø sañ" – service woman at a royal
granry, and female "kyø co³" – watch woman of the royal granry, serving
under a "kyø sþkrø – headman of royal granry, who had to look after it. The fact
was illustrated by such descriptions as "kø sañ Ui Cawy Sa³ 4" found also in
the above-mentioned "sa³lya³ Ui Kap Sa³ Khya³ " inscription. and "Uiw
Plañ kic³5 "found in the "Rajama³galamahæpatiy " inscription inscribed in
AD 1233. Thus it can be deduced that women of Bagan period participated,
equally with men, in the service of financial sector of administration.
Chiefs of the group of association were known as "sa³krø " and
"sa³lya³ ". Besides male sa³krøor male sa³lya³, it was found that there were
female sa³krø or sa³lya³ as well. In this regard, the honorary title, "sa³krø "
was also found associated with the title (name) of monks6. With respect to this
this fact, Dr. Than Tun explained in his work Khithaung Myanmar Rajawin-
Ancient Myanmar History, that
…If the term "sa³krø " is applied to Rahan-monk only, "sa³ " means
sa³ghæ , and it may be said to assume that it implies "sa³ghæthaera ".
As it is not so, however, it renders very difficult to interpret the
meaning. So far as it is known now, a "sa³krø " is a respectable person
whether he is a lay man or monk. It is to be considered that a lay man
sa³krø is responsible for administration.7"
According to Daw Than Swe's article, entitled: "Myanmar Language,
Myanmar inscription", the interpretation was:-
1 PL 196
1
2 PL 40
16-17
3 Nyein Maung, U, Shayhaung Myanmar Kyauksarmyar (Ancient Myanmar Stone
Inscriptions), Vol. I, Yangon, Govt Press, 1972.
4 PL 40
19
5 PL 68
19
6 PL 6
9
7 Than Tun, 1969, p. 145.
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Kalay University Research Journal
Sa³ikrø- Chief of a group, society of an association; leader of Rahan-
Monks.
Sa³lya³ -Assistant chief of a group, society or an association1.
U Thein Hlaing's Dictionary of Ancient Myanmar Historical Research defines
the terms as follows:-
"Sa³krø "– (inscription) means
(1) A senior Sa³ghæ – monks; Mahathe – Buddhist priest of twenty or
more years of monkhood.
(2) Chief of leader of a group, society or an association2.
According to these descriptions, with regard to the usage of words
"sa³krø and sa³lya³ " the latter may be interpreted as an assistant chief of a
group, society of an association. The word "sa³krø" must consequently be
taken to mean "sa³ghæthera " only when it is found associated with titles of
sa³ghæ, but if it is used in combination with names of lay men, it should be
interpreted as a group's or society's chief who is responsible for administrative
affairs.
The study of inscriptions of the Bagan period show that there had been
female sa³krø – chief of groups or societies, who were responsible for
executive affairs. The following inscription were cases in point:
"Sa³krø Uiw, Khyam, sæ³ 3" was found in the 'Ca Khi Phu Næ'
inscription, inscribed in AD 1168. "Sa³krø Ui Chum Sa³4 " was described in
the "sa³krø Ui Chum Sa³" inscription inscribed in AD 1217. The name,
"sa³kriy Uiw, Myak Ra Sa³ 5" was found in the number three inscription, in
the Han Lin Inscription Hall, inscribed in AD 1217. The name, "sa³krø Uiw,
Lhok Sa³ 6" was found in the No-33 inscription, inscribed in AD 1224, and
kept in the Mandalay Place Inscription Hall. In the same way, the name,
"sa³krø Uiw, Si Sa³"7 was found to be written in the "Uiw, Si Sa³" inscription
inscribed in AD 1224. And the word, "Sa³krø Uin Cim Sa³ 8" was found in the the 'kamkun cakhø samø" inscription inscribed in AD 1229. From these inscriptions, it can firmly be deduced that in the administration of the Bagan period there had been service women serving in sa³krø ranks.
1 Than Shwe, 1980, p. 93
2 Thein Hlaing, U. Khithaung Myanmar Thamaing Thuthethana Abidan (Acient
Myanmar History Dictionary), Yangon, Universities' Press, 2000. 3 Nyein Maung, 1972, p. 34
9
4 Lbid, p. 119
2
5 Nyein Maung, 1972, p. 123
9
6 PL 53
9
7 PL 124/a
3
8 PL 60/9
11
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Kalay University Research Journal 2010
Regarding the position of sa³lya³ - Assisstant chief of a group or a society, the following evidences were discovered:
"sa³lyæ³ Ui Kap San Khyæ³"1 was inscribed in AD 1213 in an inscription which was placed inside the wall of the Shinpin Bodi Pagoda in Bagan. The name "sa³lya³ Ui Chu Sa³ 2" was seen in the Bhui ka Lan cave-pagoda inscription inscribed in AD 1243. The word "sa³lya³ Ma Pyat Sa³ "3 was found in the couple of sukrway Ui Kram Khya³ Sa³ inscription inscribed in AD 1245.
Thus, taking into consideration that women had served in different executive ranks from the high ranking officials such as amat, sampya³ and kalan, below the post of ma³krø, to those of sa³krø and sa³lya³, conclusion may be drawn that women shared equal opportunities with men in the administration of the Bagan period.
1 PL 39
2-3
2 PL 151
4-5
3 PL 157
13
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Kalay University Research Journal
Reference
(1) Hunanan Yazawintawgyi (Glass Palace Chronicle) Vol. I, Yangon, New light of Myanmar in Guardian Press, 1992.
(2) Khin Khin Sein, Daw,"Bagankhit Amyothamimyar(Women in Bagan Period)"
Research in Burmese History No.1, Yangon, Sarpay Beikman Press, 1977.
(3) Khin Khin Sein, Daw, Bagan Khit Yinkyaehmu (The Civilization of Bagan),
Yangon Sarpay Beikman Press, 1986.
(4) Luce, G.H, "Grography of Burma under the Pagan Dynasty", JBRS, XLII, i, 1959.
(5) Luce, G.H, "Note of the peoples of Burma in the 12th
– 13th
Century AD", JBRS,
XLII, i, 1959.
(6) Luce, G.H, and Pe Maung Tin, Protfolio, I, Inscriptions of Burma I, Britian, Oxford
University Press, 1933.
(7) Luce, G.H, and Pe Maung Tin, Protfolio, II, Inscriptions of Burma II, Britian,
Oxford University Press, 1933.
(8) Luce, G.H, and Pe Maung Tin, Protfolio, III, Inscriptions of Burma III, Britian,
Oxford University Press, 1939.
(9) Luce, G.H, and Pe Maung Tin, Protfolio, IV, Inscriptions of Burma IV, Britian,
Oxford University Press, 1956.
(10) Luce, G.H, and Pe Maung Tin, Protfolio, V, Inscriptions of Burma V, Britian,
Oxford University Press, 1958.
(11) Myanmar Abidanakyinchoke (Outline of Myanmar Dictionary), Vol. IV, Yangon,
Sarpay Beikman Press, 1980.
(12) Myanmar Abidanakyinchoke (Outline of Myanmar Dictionary), Vol. V, Yangon,
Sarpay Beikman Press, 1980.
(13) Nyein Maung, U, Shayhaung Myanmar Kyauksarmyar (Ancient Myanmar Stone
Inscriptions), Vol. I, Yangon, Govt Press, 1972.
(14) Pe Maung Tin, U. Some Old Words in the Inscription, JBRS, XX, i, 1930.
(15) Than Shwe, Daw. Myanmar Bartharsakar, Myanmar Kyauksar Sarthan
Saungparmyar (Myanmar Language, Articles from Myanmar Stone Inscriptions),
Yangon, Department of Higher Education, 1980.
(16) Than Tun, Dr. Athimyin Bamathamaing(New Outlook on Myanmar History),
Mandalay, Thukhawadi Press, 1975.
(17) Than Tun, Dr. Khithaungyazawin (The Old History of Myanmar) Yangon,
Mahadagon Press 1969.
(18) Thein Hlaing, U. Khithaung Myanmar Thamaing Thuthethana Abidan (Acient
Myanmar History Dictionary), Yangon, Universities' Press, 2000.
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Kalay University Research Journal 2010
The Domination Number and the Covering Numbers
,Independence Numbers of a Graph
Moe Thu1
Abstract
We define a dominating set of a graph G and the domination number
of G, which is denoted by )G( .And then also define the degree of G, the
vertex, edge independence numbers, vertex, edge covering numbers. So we
see they relates each other and the number of vertices of G.
Definition
The order of a graph G is the number of vertices in G; it is denoted
by G . The size of a graph G is the number of edges in G. G( n , m )
denotes an arbitrary graph of order n and size m.
If U is a nonempty subset of the vertex set V(G) of a graph G, then-the
subgraph U of G induced by U is the graph having vertex set U and whose
edge set consists of those edges of G incident with two elements of U.
The degree of a vertex v in a graph G is the number of edges of G
incident with v. The degree of v is also the number of vertices in G that are
adjacent to v.
A vertex of degree 0 is also called an isolated vertex; while a vertex
of degree 1 is also referred to as an end-vertex of G.
The minimum degree of G is the minimum degree among the vertices
of G and is denoted by (G) .
The maximum degree is defined similarly and is denoted by (G) .
Suppose that the vertex-set of a graph G can be divided into two
disjoint sets V1 and V2, in such a way that every edge of G joins a vertex of V1
to a vertex of V2; G is then said to be a bipartite graph (sometimes denoted
by G (V1,V2)).
In a bipartite graph G (V1,V2), it is not necessarily true that every
vertex of V1 is joined to every vertex of V2; if however this does happen, and
if G is simple, then G is called a complete bipartite graph, usually denoted
by Kr,s where r and s are the number of vertices in V1 and V2 respectively.
1. Professor, Department of Mathematics, Kalay University
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Kalay University Research Journal
Note that Kr,s has r + s vertices and rs edges.
A complete bipartite graph of the form K1,s is called a star graph.
For a graph G and vV(G), define the neighborhood of v to be the set
N(v) y V(G) : vy E(G) .
A vertex v in a graph G is said to dominate itself and each of its
neighbors, that is, v dominates the vertices in its closed neighborhood N[v].
A set S of vertices of G is a dominating set of G if every vertex of
G is dominated by at least one vertex of S. Equivalently, a set S of vertices of
G is a dominating set if every vertex in V(G) – S is adjacent to at least one
vertex in S.
The minimum cardinality among the dominating sets of G is called
the domination number of G and is denoted by (G).
A dominating set of cardinality (G) is then referred to as a minimum
dominating set.
A minimal dominating set in a graph G is a dominating set that
contains no dominating set as a proper subset. A minimal dominating set of
minimum cardinality is, of course, a minimum dominating set and consists of
(G) vertices.
Example
The sets S1 = { v1, v2, y1, y2 } and S2 = { w1, w2, x } are both
dominating sets in the graph G of Figure 1.1 , indicated by solid circles .
Since S2 is a dominating set of minimum cardinality, γ (G) = 3. The set
S1= {v1,v2,v3,v4}is a minimal dominating set that is not a minimum
dominating set .
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Kalay University Research Journal 2010
Theorem
A dominating set S of a graph G is a minimal dominating set of G if
and only if every vertex v in S satisfies at least one of the following two
properties:
(i) there exists a vertex w in V(G) – S such that N(w) S = {v}
(ii) v is adjacent to no vertex of S .
Proof.
Suppose that each vertex v in S satisfies at least one of the properties (i)
and (ii).
If (i) holds, then there exists w V(G) – S which is not adjacent to
any vertex in S – {v}. Then S – {v} is not a dominating set of G.
If (ii) holds, then v is not adjacent to any vertex of S – {v}. Thus
S – {v} is not a dominating set of G. Therefore, S is a minimal dominating
set of G.
Conversely, assume that S is a minimal dominating set of G. Let v be
arbitrary element in S .Then S – {v} is not a dominating set of G. Hence there
is a vertex w in V(G) – (S –{v}) which is adjacent to no vertex of S – {v}.
So
N(w) S – {v} = . If w = v , then v is adjacent to no vertex of S.
If w v , then w is adjacent to at least one vertex of S because S
is a dominating set of G and w S . So w must be adjacent to v.
Hence N(w) S = {v} .
Theorem
If S is a minimal dominating set of a graph G without isolated vertices,
then V(G) – S is a dominating set of G.
Proof.
Let v S. Then v has at least one of the two properties (i) and (ii)
described in the statement of Theorem. Suppose first that there exists a vertex
w in V(G) – S such that N(w) S = {v}. Hence v is adjacent to some vertex
in V(G) – S. Suppose next that v is adjacent to no vertex in S. Then v is an
isolated vertex of the sub graph S .
Since v is not isolated in G, the vertex v is adjacent to some vertex of
V(G) – S . Thus V(G) – S is a dominating set of G.
For graphs G without isolated vertices, we now have an upper bound
for (G) in terms of the order of G.
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Kalay University Research Journal
Corollary
If G is a graph of order n without isolated vertices , then (G) n2
.
Proof.
Let S be a minimal dominating set of G .By Theorem, V(G) – S is a
dominating set of G . Thus
(G) min { S)G(V,S } n2
.
Theorem
Let G be a graph of order n with = (G) > 1.
Then n (1 ln ( 1) )
(G)1
.
Proof.
From a random vertex subset S V(G) by including each vertex
independently with probability p = ln ( +1 ) / ( +1). Given S, let T be the
set of vertices outside S having no neighbor in S; adding T to S yields a
dominating set.The experiment gives us both S and T, so we seek the expected
size of the union. Since each vertex appears in S with probability p, E( S ) =
np. The random variable T is the sum of n indicator variables for whether
individual vertices belong to T. We have v T if and only if v and its
neighbors all fail to be in S, the probability of which is bounded by ( 1 – p
) +1
, since v has degree at least . Since )1(p1 e)p1( , we have
E ( S + T ) np + n )1(pe
= np + n)1(
1
)1(ln
e
= np + n 1)1(lne
= n [ 1ln ( 1)( 1)
1
]
= n [ ln ( 1) 1
1 1
]
= n ( 1 ln ( 1 ) )
1
.
We have a dominating set S T of G whose cardinality is
at most n ( 1 ln ( 1 ) )
1
.
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Kalay University Research Journal 2010
So, n (1 ln ( 1) )
(G)1
.
Theorem
Every graph G without isolated vertices contains a minimum
dominating set S such that for every vertex v of S, there exists a vertex w of
G – S such that N ( w ) S ={ v } .
Proof .
Let S be one of the minimum dominating sets such that S has
maximum size. Suppose, to the contrary, that S contains a vertex v that does
not have the desired property. Then by Theorem 1.3, v is an isolated vertex in
S . Moreover, every vertex of V(G) – S that is adjacent to v is adjacent to
some other vertex of S as well. Since G contains no isolated vertices, v is
adjacent to a vertex w in V(G) – S. Consequently, ( S – {v}) {w} is a
minimum dominating set of G whose induced sub graph contains at least one
edge incident with w and hence has a greater size than S . This produces a
contradiction.
Theorem
If G is a graph of order n, then n1 (G)
.)G(n)G(
Proof.
Let S be a minimum dominating set of G. Every vertex w V(G) – S
is adjacent to at least one of the vertex of S. So w N(v) for some v S. If
the vertices of S are isolated, then V(G) – S v S
N(v)
. If S has no isolated
vertices, then V(G) – S v S
N(v)
. So V(G) – S v S
N(v)
.
Hence SS)G(V )G( . Therefore, n – )G()G()G( and so
n(G)1 (G)
.
Next we establish the upper bound. Let v be a vertex of G with
deg v = )G( . Then V(G) – N(v) is a dominating set of cardinality
n )G( ; so )G(n)G(
Definition
If G is connected, we define the vertex-connectivity )G( of G to
be the size of the smallest separating set in G; in other words, )G( is the
smallest number of vertices we can delete in order to disconnect G.
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Kalay University Research Journal
Two vertices that are not adjacent in a graph G are said to be
independent. A set S of vertices is independent if every two vertices of S are
independent.
The vertex independence number or simply the independence
number (G) of a graph G is the maximum cardinality among the
independent sets of vertices of G.
An independent set of edges in a graph G is a set of edges, each two
of which are independent ( nonadjacent ). The edge independence number
1 (G) of G is the maximum cardinality among the independent sets of edges
of G.
A vertex and an edge are said to cover each other in a graph G if they
are incident in G. A vertex cover in G is a set of vertices that covers all the
edges of G.
An edge cover in a graph G without isolated vertices is a set of edges that
covers all vertices of G.
The minimum cardinality of a vertex cover in a graph G is called the
vertex covering number of G and is denoted by )G( . The edge covering
number 1 (G) of a graph G ( without isolated vertices ) is the minimum
cardinality of an edge cover in G . For s t, we have )K( t,s = s and
)K( t,s1 = t. As another illustration of these four parameters, we note that
for n 1)K(,2 n , )K( n1 = n2
, )K( n = n – 1 and )K( n1 =
n2
. In Figure 1.2 , we see that )K( 5 = 1, )K( 51 = 2 , )K( 5 = 4 ,
)K( 51 = 3 .
Figure 1.2
Theorem
For every graph G , (G) )G( (G) .
Theorem
If G is a graph of order n, then (G)κ-n)G(γ ≤ .
1
5
3 4
2
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Kalay University Research Journal 2010
Proof.
From Theorem , )G(κ-n≤)G(γ since )G()G( .
Theorem
If G is a graph of order n having no isolated vertices , then
n)G(β)G(αandn)G(β)G(α 11 =+=+ .
Proof.
Let U be an independent set of vertices of G with )G(U .
Clearly, the set V(G) – U is a vertex cover in G . Therefore,
)G(n)G( . If, however, W is a set of (G) vertices that covers all
edges of G , then V(G) – W is independent; thus (G) )G(n . So
(G) (G) n .
Let E1 be an independent set of edges of G with )G(E 11 .
Obviously, E1 covers 2 1 (G)-vertices of G. For each vertex of G not covered
by E1, select an incident edge and define E2 to be the union of this set of edges
and E1. Necessarily, E2 is an edge cover in G so that )G(E 12 . Also we
note that ;nEE 21 hence n)G()G( 11 . Now suppose that E
is an edge cover in G with E = )G(1 . The minimality of E implies
that each component of E is a tree. Select from each component of E
one edge, denoting the resulting set of edges by E . We observe that E
)G(1 and that E + E = n . These two facts imply that
n)G()G( 11 . So 1 1(G) (G) n .
References
[ 1 ] Bollobas .,B., “ Modern Graph Theory ”. Springer - Verlag; NewYork Inc, 1998 .
[ 2 ] Bondy , J . A . and Murty U.S.R. “ Graph Theory with Applications ”;