COMPLETE-IRREGULARITY STRENGTH OF CIRCULANT GRAPH - Anggun Pribadi, Aswan
A simple graph G = (V (G);E(G)) admits an H-covering if every edge in E(G) belongs to at least one subgraph of G isomorphic to H. A total k-labeling : V (G) [ E(G) ????! f1; 2; : : : ; kg with weight function wt (G0) = X v2V (G0) (v) + X e2E(G0) (e) for any subgraphG0 ofGcalled to beH- irregular total k-labeling ofGif wt (H0) 6= wt (H00) for every two different subgraph H0;H00 of G isomorphic to H. The smallest integer k such that G has an H-irregular total k-labeling called the total H-irregularity strength of graph G and denoted by ths(G;H). In this paper, we consider a circulant graph Cin(1; 2; : : : ;m) where n 2m + 3. We also considers the case for vertex (edge) k-labeling. The smallest integer k such that G has an H- irregular vertek (edge) k-labeling called the vertex (edge) H-irreguarity strength of graph G and denoted by vhs(G;H) (ehs(G;H)). We determine an exact value of ths(G;H); vhs(G;H) and ehs(G;H) for graph G = Cin(1; 2; : : : ;m) where H is complete graphs Km+1 for some integers m 2.