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Reseach Article

Colourings in Bipartite Graphs

by Y.B.Venkatakrishnan, V.Swaminathan
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 25 - Number 3
Year of Publication: 2011
Authors: Y.B.Venkatakrishnan, V.Swaminathan
10.5120/3015-4075

Y.B.Venkatakrishnan, V.Swaminathan . Colourings in Bipartite Graphs. International Journal of Computer Applications. 25, 3 ( July 2011), 1-6. DOI=10.5120/3015-4075

@article{ 10.5120/3015-4075,
author = { Y.B.Venkatakrishnan, V.Swaminathan },
title = { Colourings in Bipartite Graphs },
journal = { International Journal of Computer Applications },
issue_date = { July 2011 },
volume = { 25 },
number = { 3 },
month = { July },
year = { 2011 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume25/number3/3015-4075/ },
doi = { 10.5120/3015-4075 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:10:46.973697+05:30
%A Y.B.Venkatakrishnan
%A V.Swaminathan
%T Colourings in Bipartite Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 25
%N 3
%P 1-6
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The concept of X-chromatic partition and hyper independent chromatic partition of bipartite graphs were introduced by Stephen Hedetniemi and Renu Laskar. We find the bounds for X-chromatic number and hyper independent chromatic number of a bipartite graph. The existence of bipartite graph with χh(G)=a and γY(G)=b-1, χh(G)=a and χX(G)=b where a ≤b are proved. We also prove the existence of bipartite graphs for any three positive integers a, b, c such that c ≥ 2(b-a)+1, there exists a graph G such that χX(G)=a, χXd(G)=b and |Y|=c. The bipartite theory of Dominator colouring is introduced.

References
  1. Gera.R, Horton.S and Ramussen.C, Dominator coloring and safe clique partition, Congressus Numerantium, Volume 181 (2006), 19-32.
  2. Haynes T.W, Hedetneimi S.T, Slater P.J, Fundamentals of domination in graphs, Marcel Dekker., Inc., 1988.
  3. Haynes T.W, Hedetneimi S.T, Slater P.J, Domination in graphs Advanced topics, Marcel Dekker., Inc., 1988.
  4. Stephen Hedetneimi, Renu Laskar, A Bipartite theory of graphs I, Congressus Numerantium, Volume 55, December 1986, 5-14.
  5. Stephen Hedetneimi, Renu Laskar, A Bipartite theory of graphs II, Congressus Numerantium, Volume 64, November 1988, 137-146.
  6. Swaminathan.V, Venkatakrishnan Y.B, Some Characterization theorems, Mathematical and computational Models, edited by R.Nadarajan et al., Narosa Publishing House, India (2008) 201-206.
Index Terms

Computer Science
Information Sciences

Keywords

X.Chromatic number hyper independent chromatic number X-dominator X-colouring of a graph