The Dominator Coloring of Central and Middle Graph of Some Special Graphs

Abstract

Let $G = (V, E)$ be an undirected graph. A dominator coloring of a graph G is a proper coloring in which every vertex of G dominates every vertex of at least one color class. The convention is that if $\{V\}$ is a color class then V dominates the color class $\{V\}$. The Dominator Chromatic number $\chi_{d}(G)$ is the minimum number of colors required for a dominator coloring of G. Here we investigate the Dominator Chromatic number of middle and central graph of Tadpole graph and Snake graph.