ON EDGE IRREGULARITY STRENGTH OF SOME GRAPHS

For a simple, connected and undirected graph G(V, E) the vertex k-labeling is a map psi : V(G) -> {1, 2, ..., k}. This map assigns a weight for each edge in E. The weight of e = uv in G is psi(e) = psi(uv) = psi(u) + psi(v). The k-labeling map psi is called an irregular k-labeling of G if the assigned edge weights are distinct. The minimum k for which the graph G has an irregular k-labeling is called the edge irregularity strength of G, denoted by es(G). The value of es(G) has been found for some graphs, such as the complete bipartite graph K-n,K- 2, the corona product of two paths P-n circle dot P-6 and the corona product of path and cycle P-n circle dot C-3. The main aim of this paper is to generalize some of the recent results. We do it by finding the exact value of the edge irregularity strength of K-n,K- m, P-n circle dot P-m and P-n circle dot C-m.