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arXiv · 2608.11723

Every 2-Subdivision of a Cubic Graph Is Antimagic

Fei-Huang Chang·Teng-Da Chang·Zhishi Pan
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Abstract

Let G be a finite simple cubic graph, not necessarily connected, and let S_2(G) be obtained by subdividing every edge of G twice. Li (2025) developed general constructions for antimagic labelings of repeated subdivisions, but the cubic case G(3) = S_2(G) is not covered by those methods. Our first proof constructs an edge labeling of G in which every vertex sum is sufficiently large and occurs at most twice, and then uses an orientation after subdivision to separate the remaining equal sums. A second, direct construction uses the same path decomposition to make the internal contribution at each original vertex constant, while a unique endpoint contribution distinguishes the resulting sums. The direct construction further shows that S_2(G) is strongly antimagic whenever every vertex of G has odd degree at least three.

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Fei-Huang Chang, Teng-Da Chang, Zhishi Pan. 2026-08-12. Every 2-Subdivision of a Cubic Graph Is Antimagic. https://arxiv.org/abs/2608.11723

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