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The Cyclic Edge Connectivity and Anti-Kekulé Number of the (5,6,7)-Fullerene
Polycyclic Aromatic Compounds ( IF 2.4 ) Pub Date : 2017-11-14 , DOI: 10.1080/10406638.2017.1382543
Shengzhang Ren 1, 2 , Tingzeng Wu 3 , Heping Zhang 1
Affiliation  

ABSTRACT A plane cubic graph is called a (5,6,7)-fullerene if its faces are only composed of pentagons, hexagons and heptagons. In this paper, we completely characterize the cyclic edge-connectivity of the (5,6,7)-fullerene. Furthermore, we obtain that the anti-Kekulé number of the (5,6,7)-fullerene is 4 when the cyclic edge-connectivity is larger then three. In particular, we obtain some properties with respect to the anti-Kekulé number of the (5,6,7)-fullerene with cyclic 3 edge-connectivity if it is 2-extendable.

中文翻译:

(5,6,7)-富勒烯的循环边连通性和反凯库乐数

摘要 如果平面立方图的面仅由五边形、六边形和七边形组成,则称为 (5,6,7)-富勒烯。在本文中,我们完整地表征了 (5,6,7)-富勒烯的循环边连通性。此外,当循环边连通性大于 3 时,我们得到 (5,6,7)-富勒烯的反凯库勒数为 4。特别是,我们获得了一些关于具有循环 3 边连接性的 (5,6,7)-富勒烯的反凯库勒数的性质,如果它是 2-可扩展的。
更新日期:2017-11-14
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