On graphs with equal domination and chromatic transversal domination numbers

Abstract

Let ϰ(G) denote the chromatic number of a graph G = (V,E). A dominating set D (Formula presented) V(G) is a set such that for every vertex v (Formula presented)V(G)\D there is at least one neighbor in D. The domination number γ(G) is the least cardinality of a dominating set of G. A chromatic transversal dominating set(CTDS) of a graph G is a dominating set D which intersects every color class of each ϰ-partition of G. The chromatic transversal domination number γct (G) is the least cardinality of a CTDS of G. In this paper, we characterize cubic graphs, block graphs and cactus graphs with equal domination number and chromatic transversal domination number .