Vertex-distinguishing proper edge-colorings

An edge-coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for a vertex-distinguishing proper edge-coloring of a simple graph G is denoted by . A simple count shows that where ni denotes the number of vertices of degree i in G. We prove that where C is a constant depending only on Δ. Some results for special classes of graphs, notably trees, are also presented. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 73–82, 1997