Orientable ℤN-Distance Magic Graphs

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Let G = (V, E) be a graph of order n. A distance magic labeling of G is a bijection : V → {1, 2, . . ., n} for which there exists a positive integer k such that ∑xN(v) (x) = k for all vV, where N(v) is the open neighborhood of v.

Tuttes flow conjectures are a major source of inspiration in graph theory. In this paper we ask when we can assign n distinct labels from the set {1, 2, . . ., n} to the vertices of a graph G of order n such that the sum of the labels on heads minus the sum of the labels on tails is constant modulo n for each vertex of G. Therefore we generalize the notion of distance magic labeling for oriented graphs.

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Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

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Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs


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