A note on complementary tree domination number of a tree

B. Krishnakumari, Y. B. Venkatakrishnan

Resumen


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.

Palabras clave


Dominating set ; Complementary tree dominating set ; Edge-vertex dominating set ; Tree.

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Referencias


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

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