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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.2 Antofagasta June 2015

http://dx.doi.org/10.4067/S0716-09172015000200002 

A note on complementary tree domination number of a tree

B. Krishnakumari

Y. B. Venkatakrishnan

SASTRA University

India 


ABSTRACT

A complementary tree dominating set of a graph G, is a set D of vertices of G such that D is a dominating set and the induced sub graph (V \ D) is a tree. The complementary tree domination number of a graph G, denoted by γctd(G), is the minimum cardinality of a complementary tree dominating set of G. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is incident with an edge of D or incident with an edge adjacent to an edge of D. The edge-vertex domination number of a graph, denoted by γev (G), is the minimum cardinality of an edge-vertex dominating set of G. We characterize trees for which γ(T) = γctd(T) and  γctd(T) = γev(T) + 1.

Keywords : Dominating set; Complementary tree dominating set; edge-vertex dominating set; tree.

AMS Subject Classification : 05C69.


REFERENCES

[1]    T. Haynes, S. Hedetniemi and P. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, (1998).         [ Links ]

[2]    T. Haynes, S. Hedetniemi and P. Slater (eds.), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, (1998).         [ Links ]

[3]    X. Hou, A characterization of trees with equal domination and total domination numbers, Ars Combinatoria 97A, pp. 499-508, (2010).         [ Links ]

[4]    M. Krzywkowski, On trees with double domination number equal to 2-domination number plus one, Houston Journal of Mathematics 39, pp. 427-440, (2013).         [ Links ]

[5]    S. Muthammai, M. Bhanumathi and P. Vidhya, Complementary tree Domination number of a graph, International Mathematical Forum 6, pp. 1273-1282, (2011).         [ Links ]

[6]    J. Peters, Theoretical and Algorithmic Results on Domination and connectivity, Ph. D. Thesis, Clemson University, (1986).         [ Links ]

B. Krishnakumari

Department of Mathematics School of Humanities and Sciences SASTRA University,

Thanjavur-613 401,

Tamilnadu,

India

e-mail : krishnakumari@maths.sastra.edu

and

Y. B. Venkatakrishnan

Department of Mathematics School of Humanities and Sciences SASTRA University,

Thanjavur-613 401,

Tamilnadu,

India

e-mail : ybvenkatakrishnan2@gmail.com

Received : August 2014. Accepted : April 2015

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