Unicyclic graphs with equal domination and complementary tree domination numbers
DOI:
https://doi.org/10.4067/S0716-09172016000300002Keywords:
Domination, complementary tree domination, unicyclic graphs, dominación, dominación complementaria de árboles, grafos unicíclicosAbstract
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.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).
[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.
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