Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1905.06595 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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].