Research Article
Colourings in Bipartite Graphs
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 25 - Issue 3 |
| Published: July 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 },
year = { 2011 },
volume = { 25 },
number = { 3 },
pages = { 1-6 },
doi = { 10.5120/3015-4075 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2011
%A Y.B.Venkatakrishnan
%A V.Swaminathan
%T Colourings in Bipartite Graphs%T
%J International Journal of Computer Applications
%V 25
%N 3
%P 1-6
%R 10.5120/3015-4075
%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
- Gera.R, Horton.S and Ramussen.C, Dominator coloring and safe clique partition, Congressus Numerantium, Volume 181 (2006), 19-32.
- Haynes T.W, Hedetneimi S.T, Slater P.J, Fundamentals of domination in graphs, Marcel Dekker., Inc., 1988.
- Haynes T.W, Hedetneimi S.T, Slater P.J, Domination in graphs Advanced topics, Marcel Dekker., Inc., 1988.
- Stephen Hedetneimi, Renu Laskar, A Bipartite theory of graphs I, Congressus Numerantium, Volume 55, December 1986, 5-14.
- Stephen Hedetneimi, Renu Laskar, A Bipartite theory of graphs II, Congressus Numerantium, Volume 64, November 1988, 137-146.
- 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.
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