Trees Whose Even-Degree Vertices Induce a Path are Antimagic

An of a connected graph is a bijection from the set of edges ) to {1, 2, . . ., | )|} such that all vertex sums are pairwise distinct, where the at vertex is the sum of the labels assigned to edges incident to . A graph is called if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than is antimagic; however the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [ , Discrete Math. 331 (2014) 9–14].