Antimagic orientation of Halin graphs

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 an 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. Hefetz, Mütze and Schwartz conjectured every connected undirected graph admits an antimagic orientation. In this paper, we support this conjecture by proving that every Halin graph admits an antimagic orientation.