Dominator Chromatic Number of Circular-Arc Overlap Graphs

Abstract

A dominator coloring problem of the graph G is a proper coloring of the graph, where every vertex of the graph inevitably dominates an entire color class. It is observed that the number of color classes selected is of minimum order and when only it suits to be the dominator chromatic number. The present paper brings to the fore, the findings related to dominator chromatic number of some special classes of circular-arc overlap graphs, upholding the concepts on the bounds of dominator chromatic number and the relation between the chromatic number and the dominator chromatic number.

Keywords: Circular-arc overlap graphs, independent set, chromatic number, dominator chromatic number