THE DOM-CHROMATIC NUMBER OF A GRAPH

B. Chaluvarajua,* and Appajigowda C. b

THE DOM-CHROMATIC NUMBER OF A GRAPH

Authors :

B. Chaluvaraju^a,* and Appajigowda C. ^b

Author Address :

^a,bDepartment of Mathematics, Bangalore University, Jnanabharathi Campus, Bengaluru - 560 056, India.

*Corresponding author.

Abstract :

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

Keywords :

Graph; Chromatic number; Domination number; Dom-chromatic number.

DOI :

Article Info :

Received : November 20, 2015; Accepted : January 01, 2016.