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| Main Authors: | , , , |
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| Format: | Preprint |
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2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1905.06595 |
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| _version_ | 1866913344273776640 |
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| author | Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín |
| author_facet | Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín |
| contents | An antimagic labeling a connected graph $G$ is a bijection from the set of edges $E(G)$ to $\{1,2,\dots,|E(G)|\}$ 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 $K_2$ 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_06595 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Trees whose even-degree vertices induce a path are antimagic Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín Combinatorics 05C78, 05C05 An antimagic labeling a connected graph $G$ is a bijection from the set of edges $E(G)$ to $\{1,2,\dots,|E(G)|\}$ 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 $K_2$ 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]. |
| title | Trees whose even-degree vertices induce a path are antimagic |
| topic | Combinatorics 05C78, 05C05 |
| url | https://arxiv.org/abs/1905.06595 |