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 $\{1,2,3,\dots ,|V(G)|+|E(G)|\}$ 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 $\{1,2,\dots ,|V(G)|\}$ 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.