Antimagic labeling and canonical decomposition of graphs

Abstract

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from { 1 , … , m } to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K 2 has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomposition introduced by Tyshkevich. As a consequence, we provide a sufficient condition on graph degree sequences to guarantee an antimagic labeling.