On the Vertex-Distinguishing Edge Chromatic Number of 𝐏𝐦 ∨ 𝐂𝐧

Abstract

A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different, and the number of edges in any two color classes differ by at most one, which the required minimum number of colors is called the adjacent strong equitable edge chromatic number. In this paper, we present the edge coloring of join-graphs about path and cycle, and gain the vertex-distinguishing edge chromatic number of 𝑃𝑚 ∨ 𝐶𝑛.