Distance edge coloring of the Kronecker product of some graphs

Abstract

Given a graph G = (V,E), an l-edge coloring of G is a function from the edges E to colors {1,2,...k } such that any two edges within distance ¿ of each other are assigned different colors. In this paper, we determine bounds and exact values of k for the Kronecker product of two paths, two cycles, a path by a cycle, two stars and the graph K₂ by other graphs.