纳米管和环面多六边形的共振图
The resonance graphs of nanotubes and toroidal polyhexes
- School of Mathematics and Statistics, Lanzhou University（兰州大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对一般纳米管和环面多六边形，通过加强割集流和梯子条件，给出了两个完美匹配位于同一共振图连通分量的有效判据，并利用环面上简单环的同伦类简化了交替六边形情形。
AI中文摘要：
冠状体系、纳米管和环面多六边形（或富勒烯）均可视为由碳原子以六边形形状连接而成的碳网络。冠状体系和纳米管的共振图不一定是连通的。对于冠状体系和初等纳米管，作者通过使用割集上的流，给出了两个完美匹配位于共振图同一连通分量中的判据（Discrete Appl. Math. 395 (2026) 443-455）。然而，该判据的充分性对于一般纳米管和环面多六边形并不成立。本文加强这一要求，以获得纳米管（分别地，环面多六边形）的两个完美匹配位于其共振图同一连通分量中的有效判据：它们沿x轴（分别地，经线和纬线）的割集上的流相同，且梯子相同。对于环面多六边形，我们的方法使用环面上简单环的同伦类，并且对于两个完美匹配具有交替六边形的情形，上述判据可仅使用简单流加以简化。
英文摘要：
Coronoid systems, nanotubes and toroidal polyhexes (or fullerenes) can all be regarded as carbon networks composed of carbon atoms linked in hexagonal shapes. The resonance graphs of coronoid systems and nanotubes are not necessarily connected. For coronoid systems and elementary nanotubes, by using flow across cuts the present authors gave criteria for two perfect matchings lying in the same connected component of the resonance graph (Discrete Appl. Math. 395 (2026) 443-455). However, the sufficiency of such criterion does not hold for general nanotubes and toroidal polyhexes. In this paper we strengthen this requirement to obtain valid criteria for two perfect matchings of a nanotube (resp. toroidal polyhex) to lie in the same connected component of its resonance graph: they have the same flows across cuts along the $x$-axis (resp. longitude and latitude) and the same ladders. For toroidal polyhexes, our method uses homotopic classes of simple loops on the torus, and the above criterion can be simplified by using only simple flows, for the case in which two perfect matchings have alternating hexagons.
