Vertex-Magic Total Labelings

Abstract

A one-to-one map X from E ∪ V onto the integers 1, 2, …, e + v is a vertex-magic total labeling if there is a constant h so that for every vertex x, λ(x) + ∑λ(xy) = h(3.1) where the sum is over all vertices y adjacent to x. So the magic requirement is wt(x) — h for all x. The constant h is called the magic constant for λ. Again, a graph with a vertex-magic total labeling will be called vertex-magic