Orientable \mathbb{Z}_{n}-distance magic graphs
Sylwia Cichacz, Bryan Freyberg, Dalibor Fronček · Discussiones Mathematicae Graph Theory · 2018
Let G = (V, E) be a graph of order n.A distance magic labeling of G is a bijection ℓ : V → {1, 2, . . ., n} for which there exists a positive integer k such thatTuttes 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.