Super edge-magic labeling of volvox and pancyclic graphs

Abstract

Let G = (V, E) be a finite, simple and undirected graph with vertex set V(G) and edge set E(G), having |V(G)| = p and |E(G)| = q. A (p, q)-graph is edge-magic if there exists a bijective function f : V(G) ∪ E(G)-→ {1,2, ,...,p + q} such that f(u) -f f(uv) + f(v) = t, where t is called the magic constant or sometimes the valence of f for any edge uv ∈ E(G) of the graph G. An edge-magic total labeling f is called super edge-magic total if f(V(G)) = {1,2, .,p}. In this paper, we are dealing with the super edge-magic labeling of volvox and pancyclic graphs.