Strong Edge Coloring of Generalized Petersen Graphs

A strong edge coloring of a graphGis a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph P(n,k) with k >= 4 and n > 2 k can be strong edge colored with (at most) seven colors. Although the generalized Petersen graph P (n,k) is a kind of special graph, the strong chromatic index of P(n,k) is still unknown. In this paper, we support the conjecture by showing that the strong chromatic index of every generalized Petersen graph P(n,k) with k >= 4 and n > 2 k is at most 9.