Point-distinguishing chromatic index of the union of paths
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 χ0(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.
Keywordsgeneral edge coloring point-distinguishing general edge coloring point-distinguishing chromatic index
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