Antimagic Labelings of Forests
Johnny Sierra, Daphne Der-Fen Liu, Jessica Toy

TL;DR
This paper proves that all forests with at most one degree-2 vertex are antimagic by providing an algorithmic approach to the zero-sum partition method, extending previous results on trees.
Contribution
It introduces an algorithmic representation of the zero-sum partition method and applies it to prove a broader class of forests are antimagic.
Findings
Forests with at most one degree-2 vertex are antimagic.
Algorithmic approach to zero-sum partition method developed.
Extends antimagic results from trees to certain forests.
Abstract
An antimagic labeling of a graph is a bijection so that holds for all with , where is the set of edges incident to . We call antimagic if it admits an antimagic labeling. A forest is a graph without cycles; equivalently, every component of a forest is a tree. It was proved by Kaplan, Lev, and Roditty [2009], and by Liang, Wong, and Zhu [2014] that every tree with at most one vertex of degree-2 is antimagic. A major tool used in the proof is the zero-sum partition introduced by Kaplan, Lev, and Roditty [2009]. In this article, we provide an algorithmic representation for the zero-sum partition method and apply this method to show that every forest with at most one vertex of degree-2 is also antimagic.
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Taxonomy
TopicsGraph Labeling and Dimension Problems
