Antimagic orientation of forests

Abstract

An antimagic labeling of a digraph D with n vertices and m arcs is a bijection from the set of arcs of D to {1,2,…,m} such that all n oriented vertex-sums are pairwise distinct, where the oriented vertex-sum of a vertex is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. A graph G admits an antimagic orientation if G has an orientation D such that D has an antimagic labeling. Hefetz, Mütze and Schwartz conjectured every connected graph admits an antimagic orientation. In this paper, we support this conjecture by proving that any forest obtained from a given forest with at most one isolated vertex by subdividing each edge at least once admits an antimagic orientation.