Abstract: A proper ［k］-edge coloring σ of a graph G is a k-proper-edge-coloring of G using colors in ［k］={1,2,…,k}, let w_σ(x)denote the sum of the colors of edges incident with x, i.e., w_σ(x)=∑_e??綍xσ(e), and w_σ(x)is called the weight of the vertex x with respect to σ. A neighbor sum distinguishing edge coloring σ of G is a proper ［k］-edge coloring of G such that no pair adjacent vertices receive the same weight. The smallest value k for which G has such a coloring is called the neighbor sum distinguishing edge chromatic number of G and denoted by χ'_∑(G). The exact values of the neighbor sum distinguishing edge chromatic number of the join of two paths with different orders are given. The upper bound of the neighbor sum distinguishing edge chromatic number of the join of two paths with same orders is obtained.

Key words: path, join, neighbor sum distinguishing edge coloring, neighbor sum distinguishing edge chromatic number