Geodesic
Trees Whose Even-Degree Vertices Induce a Path are Antimagic
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 959-966

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An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to 1, 2, . . ., |E(G)| such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 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 [Anti-magic labeling of trees, Discrete Math. 331 (2014) 9–14].
Keywords: antimagic labeling, tree 
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Lozano, Antoni; Mora, Mercè; Seara, Carlos; Tey, Joaquín. Trees Whose Even-Degree Vertices Induce a Path are Antimagic. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 959-966. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a16/