低阶富勒烯图的匹配强迫谱和反强迫谱的连续性
Continuity of Matching Forcing Spectra and Anti-Forcing Spectra for Lower-Order Fullerenes
DOI: 10.12677/AAM.2023.123119, PDF,    国家自然科学基金支持
作者: 韩 慧, 周玉玉, 王彦通*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 富勒烯图；强迫谱；反强迫谱；整数线性规划；连续性；Fullerene； Forcing Spectrum； Anti-Forcing Spectrum； Integer Linear Programming； Continuity
摘要: 富勒烯图的凯库勒结构的内、外自由度，对应于图的完美匹配的强迫数与反强迫数，可用于衡量化学分子的稳定性。由于使用穷举法计算比较大的分子图给定完美匹配的反强迫数时过于耗时，因此本文选用相对高效的整数线性规划法计算了C20，C24，C26，...，C58的所有3958个同分异构体的匹配强迫谱和反强迫谱，据此给出了它们的连续性，并将相应的结果汇总成了一系列表格和折线图。本文的工作将为富勒烯图的稳定性等研究提供一些理论参考。
Abstract: The innate and external degrees of freedom of the Kekulé structure of fullerenes, corresponding to the forcing number and anti-forcing number of the perfect matching of graphs, can be used as a measure of molecular stability. The exhaustive method is too time-consuming to calculate the an-ti-forcing number of the perfect matching of large graphs. Therefore, this paper uses efficient inte-ger linear programming to calculate the forcing spectrum and anti-forcing spectrum of all 3958 isomers of C20，C24，C26，...，C58 , gives their continuity, and summarizes the results into a series of ta-bles and line charts. The work presented in this paper will provide some theoretical references for studying the stability of fullerenes.
文章引用：韩慧, 周玉玉, 王彦通. 低阶富勒烯图的匹配强迫谱和反强迫谱的连续性[J]. 应用数学进展, 2023, 12(3): 1173-1187. https://doi.org/10.12677/AAM.2023.123119

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