Characterizing the fullerene graphs with the minimum forcing number 3
Characterizing the fullerene graphs with the minimum forcing number 3
复制标题
用最小受力数 3 表征富勒烯图
DOI：
10.1016/j.dam.2021.02.001
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发表时间：
2021
影响因子：
1.1
通讯作者：
Lin Ruizhi
中科院分区：
文献类型：
--
作者：
Shi Lingjuan;Zhang Heping;Lin Ruizhi
图G的最小强迫数是G的唯一完美匹配中同时包含的最小边数。Zhang et al.（2010）提出任何富勒烯图的最小强迫数的界为3。然而，我们发现存在一个例外的富勒烯F24，其最小强迫数为2。在本文中，我们用构造方法表征了所有最小强迫数为3的富勒烯。这也解决了Zhang等人提出的一个开放性问题。我们还发现，除F24外，所有反强迫数为4的富勒烯都具有。最小强迫数3。特别是（4,2）型纳米管富勒烯就是这样的富勒烯。
The minimum forcing number of a graph G is the smallest number of edges simultaneously contained in a unique perfect matching of G. Zhang et al. (2010) claimed that the minimum forcing number of any fullerene graph was bounded below by 3. However, we find that there exists exactly one exceptional fullerene F24 with the minimum forcing number 2. In this paper, we characterize all fullerenes with the minimum forcing number 3 by a construction approach. This also solves an open problem proposed by Zhang et al. We also find that except for F24, all fullerenes with anti-forcing number 4 have the.minimum forcing number 3. In particular, the nanotube fullerenes of type (4, 2) are such fullerenes.