On Vertex-Magic Labeling of Complete Graphs

Abstract

Suppose G is a graph with vertex-set V and edge-set E. If λ is a one-to- one map from E∪V onto the integers {1 , 2, ... , e + v }, define the weight of vertex x to be wt(x) = λ (x) +∑ λ (xy), where the sum is over all vertices y adjacent to x. We say λ is a vertex-magic total labeling if there is a constant h so that for every vertex x, wt(x) = h. A graph with such a labeling is a vertex-magic graph.