On the vertex-distinguishing proper edge coloring of composition of complete graph and star

A proper k-edge coloring of a simple graph G is called k-vertex-distinguishing proper edge coloring (k-VDPEC) if for any two distinct vertices u and v of G, the set of colors assigned to edges incident to u differs from the set of colors assigned to edges incident to v. The minimum number of colors required for a vertex-distinguishing proper edge coloring of G, denoted by chi(s)'(G), is called the vertex-distinguishing proper edge chromatic number. For p >= 2 and q >= 4, we will obtain vertex-distinguishing proper edge chromatic number of composition of complete graph K-p with order p and star S-q with order q, which is pq. (C) 2013 Elsevier B.V. All rights reserved.