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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.3 Antofagasta Sept. 2016

http://dx.doi.org/10.4067/S0716-09172016000300002 

 

Unicyclic graphs with equal domination and complementary tree domination numbers

 

B. Krishnakumari

Sastra University, India

Y. B. Venkatakrishnan

 Sastra University, India


ABSTRACT

Let G = (V, E) be a simple graph. A set is a dominating set if every vertex in V(G) \ D is adjacent to a vertex of D. A dominating set D of a graph G is a complementary tree dominating set if induced sub graph (V \ D) is a tree. The domination (complementary tree domination, respectively) number of G is the minimum cardinality of a dominating (complementary tree dominating, respectively) set of G. We characterize all unicyclic graphs with equal domination and complementary tree domination numbers.

Keywords : Domination, complementary tree domination, unicyclic graphs.

AmS ; Subject Classification: 05C69.


REFERENCES

[1]    T. Haynes, S. Hedetniemi and P. Slater, Fundamentals ofDomination 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]    Joanna Raczek, Unicyclic graphs with equal total and total outer-connected domination numbers, Ars Comb 118, pp. 167-178, (2015).         [ Links ]

[4]    B. Krishnakumari and Y.B. Venkatakrishnan, A note on complementary tree domination number of tree, Proyecciones Journal of Mathematics 34 (2), pp. 127-136, (2015).         [ 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 ]


Received : April 2015. Accepted : July 2016

 

B. Krishnakumari
Department of Mathematics,
School of Humanities and Sciences,
SASTRA University,

Thanjavur-613 401, Tamilnadu,
India
e-mail : krishnakumari@maths.sastra.edu

Y. B. Venkatakrishnan
Department of Mathematics,
School of Humanities and Sciences,
SASTRA University,

Thanjavur-613 401, Tamilnadu,
India
e-mail : ybvenkatakrishnan2@gmail.com

 

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