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Vertex-magic total labelings of generalized petersen graphs

Abstract:

A vertex-magic total labeling of a graph G = (V, E) with ν vertices and e edges is an assignment of the integers from 1 to ν + e to the vertices and edges of C with the property that the sum of the label on a vertex and the labels on its incident edges is a constant, independent of the choice of the vertex. In this paper we give a vertex-magic total labeling for the generalized Petersen graphs P(n, m) for all n ≥ 3, 1 ≤ m ≤ ⌊(n - 1)/2⌋.