Point-distinguishing chromatic index of the union of paths
Xiang’en Chen · Czechoslovak Mathematical Journal · 2014
Let G be a simple graph. For a general edge coloring of a graph G (i.e., not necessarily a proper edge coloring) and a vertex v of G , denote by S ( v ) the set (not a multiset) of colors used to color the edges incident to v . For a general edge coloring f of a graph G , if S ( u ) ≠ S ( v ) for any two different vertices u and v of G , then we say that f is a point-distinguishing general edge coloring of G . The minimum number of colors required for a point-distinguishing general edge coloring of G , denoted by χ 0 ( G ), is called the point-distinguishing chromatic index of G . In this paper, we determine the point-distinguishing chromatic index of the union of paths and propose a conjecture.