On dominator coloring of degree splitting graph of some graphs.

Abstract

A dominator coloring (DC) is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other class. In this paper, we obtain some results on DC in the context of degree splitting graph of Middle graph of any graph G and Mycielskian graph of some graphs. Also we find DC of degree splitting graph(ds) of Star graph families such as χd(Ds(K1,n,n,n)),χd(Ds(K1,n,n)),χd(Ds(C(K1,n))) and χd(Ds(L(K1,n,n))) respectively.