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Pure Mathematics 2026
2-管状广义富勒烯图双强迫多项式的递推求解
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Abstract:
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。
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.
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