Induced Graph Theorem on Magic Valuations

Abstract

Let $G$ be a graph. A bijection $f$ from $V(G)\cup E(G)$ to $\{1,2,\dots ,|V(G)|+|E(G)|\}$ is called a magic valuation if $f(u)+f(v)+f(uv)$ is constant for any edge $uv$ in $G$. A magic valuation $f$ of $G$ is called a supermagic valuation if $f(V(G))=\{1,2,\dots ,|V(G)|\}$. The following theorem is proved.For any graph $H$, there exists a connected graph $G$ so that $G$ contains $H$ as an induced subgraph and $G$ has a supermagic valuation.