Super Vertex-magic Total Labelings of Graphs
James A. MacDougall, Mirka Miller, Kiki Ariyanti Sugeng · FedUni ResearchOnline (Federation University Australia) · 2004
Let $G$ be a finite simple graph with $v$ vertices and $e$ edges. A vertex-magic total labeling is a bijection $\lambda$ from $V (G) \cup E(G)$ to the consecutive integers 1, 2, . . . , $v+e$ with the property that for every $x \in V (G)$, $\lambda(x) + \Sigma_y\in N(x)\lambda(xy) = k$ for some constant $k$. Such a labeling is {\em super} if $\lambda(V (G)) = {1, . . . , v}$. We study some of the basic properties of such labelings, find some families of graphs that admit super vertex-magic labelings and show that some other families of graphs do not.