Injective edge coloring of some standard graph products

Abstract

An injective [Formula: see text]-edge-coloring of a graph [Formula: see text] is an assignment [Formula: see text] of colors to the edges of [Formula: see text] such that any two edges [Formula: see text] and [Formula: see text] receive distinct colors if there exists an edge [Formula: see text] different from [Formula: see text] and [Formula: see text] such that [Formula: see text] is incident on [Formula: see text] and [Formula: see text] is incident on [Formula: see text]. The least number of colors required by any injective edge coloring of [Formula: see text] is called the injective chromatic index of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we give tight upper bounds of the injective chromatic index of various standard graph products and operations, including the Cartesian product, lexicographic product, corona product, edge corona product, join, subdivision and Mycielskian of a graph.