Strong edge chromatic index of the generalized Petersen graphs

A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are adjacent to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted by χs′(G), is the minimum number of colors needed for a strong edge coloring of G. We determine the strong chromatic index of the generalized Petersen graphs P(n, k) when 1 ≤ k ≤ 3.