On the Harmonious Chromatic Number of P(αa, Kn), P(α, K1,n), p(α, Km,n)

Abstract

An harmonious m-coloring of a graph G is a vertex coloring of G that uses m colors such that adjacent vertices have different colors and each pair of colors appears together on at most one edge. The harmonious chromatic number is the minimum number n of colors such that G has an n-harmonious coloring. In this paper the harmonious chromatic number is obtained for the permutation graphs P(α, K_n), P(α, K_1,n), P(α, K _m,n).