AVD-edge coloring on powers of paths

In a proper edge coloring of a graph, the set of colors of a vertex v is the set of colors of the edges incident to v, C(v). If C(u)≠C(v) for every adjacent vertices u and v, this edge coloring is an AVD-edge coloring. The least number of colors for which G has an AVD-edge coloring is called the AVD-chromatic index, χa′(G). We determine the AVD-chromatic index for the powers of paths.