Every 2-Subdivision of a Cubic Graph Is Antimagic

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.