Magic Graphs with Pendant Edges

Abstract

A graph \(G\) is edge-magic if there exists a bijection \(f\) from \(V(G) \cup E(G)\) to \(\{1, 2, 3, \ldots, |V(G)| + |E(G)|\}\) such that for any edge \(uv\) of \(G\), \(f(u) + f(uv) + f(v)\) is constant. Moreover, \(G\) is super edge-magic if \(V(G)\) receives \(\{1, 2, \ldots, |V(G)|\}\) smallest labels. In this paper, we propose methods for constructing new (super) edge-magic graphs from some old ones by adding some new pendant edges.