On the new families of (super) edge-magic graphs

Abstract

A graph G is edge-magic if there exists a bijection f: V(G) U E(G) → {1,2,3, ⋯, |V(G)| + |E(G)|} such that for any edge uv of G, f(u)+f(uv) + f(v) is equal to a constant k, called the magic constant of f. Moreover, G is said to be super edge-magic if f(V(G)) = {1,2,3, ⋯, |V(G)|}. These concepts were first introduced by Kotzig and Rosa (1970) and Enomoto, Llado, Nakamigawa, and Ringel (1998), respectively. In this paper, we propose methods for constructing new (super) edge-magic graphs from some old ones.