A Study of Anti-Magic Graphs on Corona Product of Complete Graphs and Complete Bipartite Graphs

Abstract

Graph labeling has a wide range of applications such as coding theory, X-ray crystallography, network design, and circuit design. It can be done by assigning numbers to edges, vertices or to both. An anti-magic labeling of a graph \(G\) is a one-to-one correspondence between the edge set \(E(G)\) and the set \(\{1,2,3,\dots ,|E|\}\) such that the vertex sums are pairwise distinct. The vertex sum is the sum of labels assigned to edges incident to a vertex. Corona product of the graphs \(H\) and \(T\) is the graph \(H\odot T\) which is obtained by taking one copy of \(H\) and \(|V(H)|\) copies of \(T\) and making the \(i\)th vertex of \(H\) adjacent to every vertex of the $i$th copy of \(T\), \(1\le i\le |V(H)|\). In this study, we prove that the Corona product \(K_n\odot K_{m,m}\) generates anti-magic graphs. We also develop a programme using Matlab to demonstrate this anti-magic property.