## EDGE-VERTEX DOMINATION AND TOTAL EDGE DOMINATION IN TREES

## EDGE-VERTEX DOMINATION AND TOTAL EDGE DOMINATION IN TREES

*H. N. Kumar, Y. B. Venkatakrishnan*

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## Abstract

An edge e ∈ E(G) dominates a vertex v ∈ V (G) if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is edge-vertex dominated by an edge of D. The edge-vertex domination number of a graph G is the minimum cardinality of an edge-vertex dominating set of G. A subset D ⊆ E(G) is a total edge dominating set of G if every edge of G has a neighbor in D. The total edge domination number of G is the minimum cardinality of a total edge dominating set of G. We characterize all trees with total edge domination number equal to edge-vertex domination number.

## Keywords

Edge-vertex domination, Total Edge Domination, Tree.