SUPER EDGE-MAGIC GRAPHS

Abstract

For a graph , a bijection $f$ from $V\left(G\right){\cup }^{\text{}}E\left(G\right)$ to $\left\{1,2,\cdots ,\left|V\left(G\right)\right|+\left|E\left(G\right)\right|\right\}$ is called an edge-magic labeling of $\text{Θ}(x)$ if $f\left(u\right)+f\left(v\right)+f\left(uv\right)$ is independent on the choice of the edge $uv$. An edge-magic labeling is called super edge-magic if $f\left(V\left(G\right)\right)=\left\{1,2,\cdots ,\left|V\left(G\right)\right|\right\}$. A graph $G$ is called edge-magic (resp. super edge-magic) if there exists an edge-magic (resp. super edge-magic) labeling of $G$. In this paper, we investigate whether several families of graphs are (super) edge-magic or not. We also give several conjectures.