2-管状广义富勒烯图双强迫多项式的递推求解
Recursive Solving of Di-Forcing Polynomials for 2-Tubular Generalized Fullerene Graphs
DOI: 10.12677/pm.2026.161016, PDF,    国家自然科学基金支持
作者: 王海艳, 蔡文田：西北师范大学数学与统计学院，甘肃 兰州；俞德龙*：兰州市第六十一中学，甘肃 兰州
关键词: 2-管状广义富勒烯图；完美匹配；双强迫多项式；强迫多项式；反强迫多项式；递推公式；2-Tubular Generalized Fullerene Graph； Perfect Matching； Di-Forcing Polynomial； Forcing Polynomial； Anti-Forcing Polynomial； Recurrence Formula
摘要: 2-管状广义富勒烯图是由两端的两个两边形和两个五边形构成的帽子和纯由六边形构成的管身接成的管状广义富勒烯图。图的双强迫多项式是关于该图的所有完美匹配的强迫数和反强迫数的二变量多项式。通过对给定顶点关联边的匹配情况的分类讨论和计数，得出了2-管状广义富勒烯图双强迫多项式的线性递推公式，通项公式以及生成函数。
Abstract: The 2-tubular generalized fullerene graph is a tubular generalized fullerene graph formed by connecting a cap composed of two digons and two pentagons at each end to a tube body composed purely of hexagons. The di-forcing polynomial of the graph is a two-variable polynomial regarding the forcing numbers and anti-forcing numbers of all perfect matchings of the graph. By classifying and counting the matching situations of the edges incident to a given vertex, we derived the linear recurrence formula, general term formula, and generating function for the di-forcing polynomials of 2-tubular generalized fullerene graphs.
文章引用：王海艳, 俞德龙, 蔡文田. 2-管状广义富勒烯图双强迫多项式的递推求解[J]. 理论数学, 2026, 16(1): 127-136. https://doi.org/10.12677/pm.2026.161016

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