X− Dominating colour transversals in graphs

Resumo

Let G = (X, Y,E) be a bipartite graph. A X-dominating set D ⊆
X is called a X−dominating colour transversal set of a graph G if D is
a transversal of at least one $chi$−partition of G.The minimum cardinal-
ity of a X−dominating colour transversal set is called X−dominating
colour transversal number and is denoted by $chi_{dct}(G)$. We find the
bounds of X−dominating colour transversal number and characterize
the graphs attaining the bound.

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Biografia do Autor

Venkatakrishnan Balasubramanian Yanamandram, SASTRA University

Assistant Professor,

Department of Mathematics,

School of Humanities and Sciences,

SASTRA University


Tanjore, India

C. Natarajan, SASTRA University

Department of Mathematics

SASTRA University

India

S. K. Ayyaswamy, SASTRA University

School of Humanities and Sciences

Department of Mathematics

 

Referências

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T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs - Advanced Topics, Marcel Dekker, New York, 1998.

Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs I, Congressus Numerantium, Volume 55; December 1986, 5–14.

Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs II, Congressus Numerantium, Volume 64; November 1988, 137-146.

V. Swaminathan and Y. B. Venkatakrishnan, Bipartite theory of irredundant set, Proyecciones Journal of Mathematics, Volume 30;2011, 19-28.

V. Swaminathan and Y. B. Venkatakrishnan, Bipartite theory on domination in complement of a graph, International Journal of Computational and Mathematical Sciences, Volume 3;2009, 96-97.

Publicado
2015-06-29
Seção
Artigos