Injective edge chromatic index of generalized Petersen graph P(ck,k)

An injective [Formula: see text]-edge coloring of a graph [Formula: see text] is a [Formula: see text]-edge coloring [Formula: see text] of [Formula: see text] such that [Formula: see text] for any three consecutive edges [Formula: see text] and [Formula: see text] of a path or a 3-cycle. The injective edge chromatic index of [Formula: see text], denoted by [Formula: see text], is the minimum [Formula: see text] such that [Formula: see text] has an injective [Formula: see text]-edge coloring. Li and Chen determined the injective edge chromatic index of the generalized Petersen graph [Formula: see text] for [Formula: see text]. In this paper, we consider the injective edge coloring of the generalized Petersen graph [Formula: see text] and show that [Formula: see text] for [Formula: see text].