Abstract:

 A k-proper edge coloring of a simple graph G is called vertex-distinguishing if for two arbitrarily different vertices u and v, the set of colors assigned to the edges incident to u differs from the set of colors assigned to the edges incident to v. The minimum number of colors required for a vertex-distinguishing proper edge-coloring of a simple graph G is called the vertex-distinguishing proper edge chromatic number of G and denoted by χ′s(G). Vertex-distinguishing proper edge colorings of K3,3∨Kt are discussed.

Key words:  proper edge coloring; vertex-distinguishing proper edge coloring; vertex-distinguishing proper edge chromatic number