Proyecciones Journal of Mathematics
Vol. 30, N° 1, pp. 19-28, May 2011.
Universidad Católica del Norte
Antofagasta - Chile


Bipartite theory of irredundant set


V. Swaminathan¹
Y. B. Venkatakrishnan²

¹S. N. College, India
²Sastra university, India


Correspondencia a:

Abstract

The bipartite version of irredundant set, edge-vertex irredundant set and vertex-edge irredundant set are introduced. Using the bipartite theory of graph, IR_ve(G)+γ(G) = |V| and γ_ve(G)+IR(G) = |V| are proved.

AMS classification :05C69

Keywords : Bipartite graph, X-irredundant set, Hyper Y -irredundant set, edge-vertex and vertex-edge irredundant sets.

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References

[1] Bondy J. A., Murthy U. S. R., Graph theory with applications, London Macmillan (1976).         [ Links ]

[2] Haynes T. W., Hedetniemi. S. T. and Slater P. J., Fundamentals of Domination in graphs, Marcel Dekker, New York, (1998).         [ Links ]

[3] Jason Robert Lewis, Vertex-edge and edge-vertex parameters in graphs, (Ph. D Thesis), Clemson University, August 2007.         [ Links ]

[4] Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs I, Congressus Numerantium, Volume 55; pp. 5—14, December 1986.         [ Links ]

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

[6] Swaminathan V. and Venkatakrishnan Y. B., Hyper Y -domination in Bipartite graphs, International Mathematical Forum, Volume 4, No. 20, pp. 953-958, (2009).         [ Links ]

V. Swaminathan
Research Coordinator
Ramanujan Research Centre
S. N. College
Madurai, India
e-mail : sulanesri@yahoo.com


Y. B. Venkatakrishnan
Department of Mathematics
SASTRA University
Calicut - 673 601
Tanjore, India
e-mail : venkatakrish2@maths.sastra.edu

Received : June 2010. Accepted : December 2010