On Twin Edge Colorings of d Infinite Paths

Abstract

Let s be a proper edge coloring of a connected graph G of order at least 3, where the color set is {0,1,2,, k −1}. If s can induce a proper vertex coloring of G , then s is called a twin edge k-coloring of G . The minimum number of colors for which G has a twin edge coloring is called the twin chromatic index of G . In this paper, twin edge colorings of d infinite paths are studied, and it’s twin chromatic number is obtained.