Unicyclic graphs with equal domination and complementary tree domination numbers

Authors

  • B. Krishnakumari Sastra University.
  • Y. B. Venkatakrishnan Sastra University.

DOI:

https://doi.org/10.4067/S0716-09172016000300002

Keywords:

Domination, complementary tree domination, unicyclic graphs, dominación, dominación complementaria de árboles, grafos unicíclicos

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.

Author Biographies

B. Krishnakumari, Sastra University.

Department of Mathematics, School of Humanities and Sciences.

Y. B. Venkatakrishnan, Sastra University.

Department of Mathematics, School of Humanities and Sciences.

References

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

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

[3] Joanna Raczek, Unicyclic graphs with equal total and total outerconnected domination numbers, Ars Comb 118, pp. 167-178, (2015).

[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).

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

Published

2017-03-23

How to Cite

[1]
B. Krishnakumari and Y. B. Venkatakrishnan, “Unicyclic graphs with equal domination and complementary tree domination numbers”, Proyecciones (Antofagasta, On line), vol. 35, no. 3, pp. 245-249, Mar. 2017.

Issue

Vol. 35 No. 3 (2016)

Section

Artículos