The dom-chromatic number of a graph
B. Chaluvaraju, C. Appajigowda · Malaya Journal of Matematik · 2016
For a given $\chi$-coloring of a graph $G=(V, E)$. A dominating set $S \subseteq V(G)$ is said to be dom-coloring set if it contains at least one vertex from each color class of $G$. The dom-chromatic number $\gamma_{d c}(G)$ is the minimum cardinality taken over all dom-coloring sets of $G$. In this paper, we initiate a study on $\gamma_{d c}(G)$ and its exact values for some classes of graphs have been established. Also its relationship with other graph theoretic parameters are investigated.