Antimagic orientation of graphs with minimum degree at least 33

Abstract

AbstractAn antimagic labeling of a directed graph with vertices and arcs is a bijection from the set of arcs of to the integers such that all oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. A graph has an antimagic orientation if it has an orientation that admits an antimagic labeling. Hefetz, Mütze, and Schwartz conjectured that every connected graph admits an antimagic orientation. In this paper, we show that every bipartite graph with no vertex of degree 0 or 2 admits an antimagic orientation and every graph with minimum degree at least 33 admits an antimagic orientation.