On the Vertex-Distinguishing Equitable Edge Coloring of Product Graph

In this paper, we derive two theorems of vertex-distinguishing equitable edge coloring of product graph by using constructive method, and present the vertex-distinguishing equitable edge chromatic numbers, which the required minimum number of colors is called the vertex-Distinguishing equitable edge chromatic number of product graphs between complete graph and complete graph, star and star, wheel and wheel, which verify the conjecture on VDEECC.