The Number of Perfect Matchings in (3,6)-Fullerene

Q3 Multidisciplinary Wuhan University Journal of Natural Sciences Pub Date : 2023-06-01 DOI:10.1051/wujns/2023283192

Rui Yang, Mingzhu Yuan

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引用次数: 0

Abstract

A [see formula in PDF]-fullerene is a connected cubic plane graph whose faces are only triangles and hexagons, and has the connectivity [see formula in PDF] or [see formula in PDF]. The [see formula in PDF]-fullerenes with connectivity [see formula in PDF] are the tubes consisting of [see formula in PDF] concentric hexagonal layers such that each layer consists of two hexagons, capped on each end by two adjacent triangles, denoted by [see formula in PDF]. A [see formula in PDF]-fullerene [see formula in PDF] with [see formula in PDF] vertices has exactly [see formula in PDF] perfect matchings. The structure of a [see formula in PDF]-fullerene [see formula in PDF] with connectivity [see formula in PDF] can be determined by only three parameters [see formula in PDF], [see formula in PDF] and[see formula in PDF], thus we denote it by [see formula in PDF], where [see formula in PDF] is the radius (number of rings), [see formula in PDF] is the size (number of spokes in each layer, [see formula in PDF], [see formula in PDF] is even), and [see formula in PDF] is the torsion ([see formula in PDF]). In this paper, the counting formula of the perfect matchings in [see formula in PDF]is given, and the number of perfect matchings is obtained. Therefore, the correctness of the conclusion that every bridgeless cubic graph with [see formula in PDF] vertices has at least [see formula in PDF] perfect matchings proposed by Esperet et al is verified for [see formula in PDF]-fullerene [see formula in PDF].

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（3,6）-富勒烯的完全匹配数

富勒烯是一个连通的三次平面图形，它的面只有三角形和六边形，并且具有连通性[见PDF中的公式]或[见PDF中的公式]。具有连通性的富勒烯是由[见PDF中的公式]同心圆六边形层组成的管，这样每一层由两个六边形组成，每一端由两个相邻的三角形覆盖，用[见PDF中的公式]表示。一个[见PDF公式]-富勒烯[见PDF公式]与[见PDF公式]顶点完全匹配[见PDF公式]。(见公式的结构以PDF]富勒烯(见公式以PDF)与连接(见公式以PDF)只能由三个参数(见公式以PDF),(见公式以PDF)和(见公式以PDF),因此我们表示(见公式以PDF),其中(见公式以PDF)是半径(环),(见公式以PDF)是大小(每一层的辐条数量,(见公式以PDF),(见公式以PDF)甚至),和[见PDF公式]是扭转(见PDF公式])。本文给出了[公式见PDF]中完美匹配的计数公式，并得到了完美匹配的个数。因此，对于[见公式]-富勒烯[见公式]，验证了Esperet等人提出的每个顶点为[见公式]的无桥三次图至少具有[见公式]个完美匹配的结论的正确性。

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来源期刊

Wuhan University Journal of Natural Sciences Multidisciplinary-Multidisciplinary

CiteScore

0.40

自引率

0.00%

发文量

2485

期刊介绍： Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.