Adjacent Vertex Distinguishing Edge-colorings of the Lexicographic Product of Special Graphs

Abstract

A class of special graphs n W including wheels, fans and stars is defined. Afterwards, the adjacent vertex distinguishing edge-coloring of lexicographic product G[H] of graph class n W and any graph G is studied, and gives an upper bound of the chromatic number of coloring, For special H , the exact value of the adjacent vertex distinguishing edge-coloring of G[H] is obtained. In this paper, we prove that the chromatic number of adjacent vertex distinguishing edge-coloring of lexicographic product G[H] for any two graphs G and H is equal to the graph class n W .