Abstract

A function f : V(G) $\cup$ E(G) $\cup$ R(G) $\rightarrow$ C is said to be perfect coloring of the graph G, if f(x) $\neq$ f(y) for any two adjoint or incident elements x,y $\in$ V(G) $\cup$ E(G) $\cup$ R(G). And the PC number $\chi^{P}(G)$ is the least number of colors needed to assign colors to a graph by using perfect coloring. In this paper, we prove the results for perfect chromatic number of corona product (PCCP) of circular (cycle) graph family and a fan graph, which leads to perfect chromatic number equivalent to $\Delta$+1, where $\Delta$ is the largest degree of the resultant graph.

Keywords and Phrases

Graph coloring, corona product, perfect coloring.

A.M.S. subject classification

05.

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