Dominator and total dominator coloring of circulant graph Cn (1, 2)

Abstract

A dominator coloring (resp. total dominator coloring) of a graph G is a proper coloring of the vertices of G in which each closed neighborhood (resp. open neighborhood) of every vertex of G contains a color class. The dominator chromatic number (resp. total dominator chromatic number) of G is the minimum number of colors required for a dominator coloring (resp. total dominator coloring) of G. In this paper, we determine the dominator chromatic number and total dominator chromatic number of the circulant graph Cn (1, 2).