Caterpillars Have Antimagic Orientations

Antoni Lozano

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arXiv · 1708.02607

Caterpillars Have Antimagic Orientations

Antoni Lozano

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Abstract

An antimagic labeling of a directed graph $D$ with $m$ arcs is a bijection from the set of arcs of $D$ to $\{1,\dots,m\}$ such that all oriented vertex sums of vertices in $D$ are pairwise distinct, where the oriented vertex sum of a vertex $u$ is the sum of labels of all arcs entering $u$ minus the sum of labels of all arcs leaving $u$. Hefetz, M\"utze, and Schwartz conjectured that every connected graph admits an antimagic orientation, where an antimagic orientation of a graph $G$ is an orientation of $G$ which has an antimagic labeling. We use a constructive technique to prove that caterpillars, a well-known subclass of trees, have antimagic orientations.

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Antoni Lozano. 2017-08-08. Caterpillars Have Antimagic Orientations. https://arxiv.org/abs/1708.02607

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