# Trees whose even-degree vertices induce a path are antimagic

## TL;DR

This paper proves that a specific class of trees, where even-degree vertices form a path, are antimagic, thus extending previous results and contributing to the understanding of the antimagic labeling conjecture.

## Contribution

It establishes that trees with even-degree vertices inducing a path are antimagic, expanding the class of known antimagic trees.

## Key findings

- Trees with even-degree vertices forming a path are antimagic.
- Extends previous results by Liang, Wong, and Zhu.
- Supports the broader conjecture that all trees are antimagic.

## Abstract

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].