Split and Non-Split Dominator Chromatic Numbers and Related Parameters

Abstract

A proper graph coloring is defined as coloring the nodes of a graph with the minimum number of colors without any two adjacent nodes having the same color. Dominator coloring of G is a proper coloring in which every vertex of G dominates every vertex of at least one color class. In this paper, new parameters, namely strong split and non-split dominator chromatic numbers and block, cycle, path non-split dominator chromatic numbers are introduced. These parameters are obtained for different classes of graphs and also interesting results are established.