• DOMINATOR CHROMATIC NUMBER ON SHADOW GRAPHS AND PATH UNION OF GRAPHS

Abstract

Let G = (V, E) be a simple, finite and 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 dominator chromatic number cd(G) is the minimum number of colors required for a dominator coloring of G. The shadow graph D2(G) of a connected graph G is constructed by taking two copies of G say G¢ and G² and joining each vertex v¢ in G¢ to the neighbours of the corresponding vertex v² in G². In this paper, we obtain dominator chromatic number of shadow graphs of some interesting classes of graphs and also find the dominator chromatic number of path union of graphs.