Dom-chromatic number of certain cycle related graphs

Abstract

For a given $\chi$ - colouring of a graph $G$, a dominating set $S \subseteq V(G)$ is said to be a dom-colouring set if it contains atleast one vertex of each colour class of $G$. The dom chromatic number of a graph $G$ is the minimal cardinality taken over all its dom-colouring sets and is denoted by $\gamma_{d c}(G)$. In this paper we introduce algorithms to obtain the dom-colouring and dom-chromatic number of few cycle related graphs.