On Graphs with Equal Domination and Chromatic Transversal Domination Numbers

Abstract

Let (G) denote the chromatic number of a graph G = (V,E). A dominating set D  V(G) is a set such that for every vertex v V(G) \ D there is at least one neighbor in D. The domination number (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 -partition of G. The chromatic transversal domination number ct(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 .