Research Article

Colourings in Bipartite Graphs

by  Y.B.Venkatakrishnan, V.Swaminathan
journal cover
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
PDF

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.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

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

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