PCCP of wheel graph family with null, chain, fan and cycle graph

Abstract

A function f: P(G)∪L(G)∪R(G)→C is said to be perfect coloring of the graph G, if f(x)≠f(y) for any two adjoint or incident elements x,y∈P(G)∪L(G)∪R(G). And the PC number χ^P(G) is the least colors needed to color a graph by using perfect coloring. In this paper, we prove the results for perfect coloring of corona product(PCCP) of wheel graph family with null, chain, fan and cycle graph, which leads to perfect chromatic number equivalent to ∆+1, where ∆ is the largest degree of the resultant graph in corona product.