Dominator colorings of Cartesian product of graphs

Abstract

A dominator coloring of a graph G is a proper coloring of G in which each vertex dominates all the vertices of at least one color class. The dominator chromatic number Xd{G) of G is the minimum number of colors required for a dominator coloring of G. In [Dominator Colorings of Certain Cartesian Products of Paths and Cycles, Graphs and Combinatorics, Vol. 33 No. 1 (2017) 73-83], the dominator chromatic numbers of Cartesian product graphs ftOPn and were determined. In this paper, we continue this study on Cartesian product graphs ft DP∗, P$QCn) for n > 3 and KmDKnt for m, n > 2. © 2018 Utilitas Mathematica Publishing Incorporated. All rights reserved.