On Star Coloring of Degree Splitting of Wheel Graph Families and Mycielskian

Abstract

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number \a (G) of G is the least number of colors needed to star color G, For a given graph G = (V(G),E(G)) with V(G) = Si U 52 U 53 U ... St U T where each Si is a set of all vertices of the same degree with at least two elements and T = V(G)-Si. The degree splitting graph of G, denoted by DS(G), is obtained by adding vertices wi, it/2,... m and joining Wi to each vertex of Si for 1 < i < t. In this paper, we find the star chromatic number for degree splitting graph of wheel graph families and Mycielskian. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.