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## Proyecciones (Antofagasta)

*Print version* ISSN 0716-0917

#### Abstract

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

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 γ_{ctd}(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 γ_{ev}(G), is the minimum cardinality of an edge-vertex dominating set of G. We characterize trees for which γ(T) = γ_{ctd}(T) and γ_{ctd}(T) = γ_{ev}(T)+ 1.

**Keywords
:
**Dominating set; Complementary tree dominating set; edge-vertex dominating set; tree.