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Proyecciones (Antofagasta)

Print version ISSN 0716-0917


KRISHNAKUMARI, B  and  VENKATAKRISHNAN, Y. B. A note on complementary tree domination number of a tree. Proyecciones (Antofagasta) [online]. 2015, vol.34, n.2, pp.127-136. ISSN 0716-0917.

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.

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