每个三次图的2-细分都是反魔术图
Every 2-Subdivision of a Cubic Graph Is Antimagic
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中文总结 AI 辅助
针对三次图2-细分的反魔术图问题，通过两种构造方法证明其为反魔术图，且当原三次图顶点度数为≥3的奇数时为强反魔术图，补充了Li(2025)方法未覆盖的三次图情况。
中文摘要 AI 辅助
设G为有限简单三次图，不一定连通，S₂(G)是通过对G的每条边细分两次得到的图。Li（2025）提出了重复细分图的反魔术标号的通用构造方法，但三次图的情况G(3)=S₂(G)未被这些方法覆盖。我们的第一个证明构造了G的边标号，使得每个顶点的和足够大且最多出现两次，随后在细分后使用定向操作分离剩余的相等和。第二个直接构造使用相同的路径分解，使每个原始顶点的内部贡献为常数，而唯一的端点贡献区分得到的和。该直接构造进一步表明，当G的每个顶点度数为至少3的奇数时，S₂(G)是强反魔术图。
英文摘要
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.
