On super edge-magicness of graphs

Abstract

Let G = (V, E) be finite, simple and undirected graphs with vertex set and edge set V(G) and E(G) respectively, having V(G) = p and E(G) = q. A (p, q)-graph is edge-magic if there exists a bijective function A : V(G) ∪ E(G) → {1,2,...,p + q} such that λ(u) + λ(uv) +λ(u)= k, for all edge uv ε E(G), where k is called the magic constant or sometimes the valence of λ. An edge-magic total labeling A is called super edge-magic total if λA(V(G)) = {1,2,..., p}. In this paper, we study the super edge-magicness of zig-zag triangle, disjoint union of combs, disjoint union of stars, and the disjoint union of a star and a banana tree.