The 2-Distance Chromatic Number of Some Wheel Related Graphs

Abstract

Let ( )EVG , be a simple and connected graph of vertex set V and edge set E. By the 2-distance chromatic number of a graph G, we mean a map ( ) { }k c GV ,1 ,2 ,3 ..., : → such that any two vertices at distance at most two from each other have different colors. The minimum number of colors in 2-distance chromatic number of G is its 2-distance chromatic number, denoted by ( ). 2 Gχ In this paper, we study the 2-distance chromatic number of some wheel related graphs, and obtain the 2-distance chromatic number of ( ), 2 nWχ ( ), 2 nFχ

2 ( )nH χ and ( )nW ,2 2 χ for .