两类Mobius带上六角系统的共振图 Alternative Title The resonance graphs of two classes of hexagonal systems on Mobius strips 赵海秀 Thesis Advisor 张和平 2016-06-03 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 六角系统 共振图 Fibonacene Mobius带 Abstract 六角系统是2-连通的平面二部图且它的每个内面都是一个正六角形, 其共振图反映了它的完美匹配的整体结构. Fibonacenes 是六角系统中的一类图. S. Klavžar和P. Žigert Pleter在2005年证明了, 任意一个含有n个六角形的 fibonacene, 它的共振图同构于斐波那契立方.在这篇论文中, 我们讨论了 Möbius带上含有n个六角形的 fibonacene 的共振图且证明了: 当n为奇数时, 其共振图同构于卢卡斯立方和两个孤立点的并; 当n为偶数时, 其共振图同构于卢卡斯立方. 进一步, 我们证明了一类 Möbius 带上六角形链的共振图同构于超立方的子图和两个孤立点的并. Other Abstract Hexagonal systems are 2-connected bipartite plane graphs with every inner face a positive hexagon and their resonance graphs reflect the massive structure of their perfect matchings. Fibonacenes are a class of graphs in hexagonal systems. In 2015, S. Klavžar and P. Žigert Pleter have proved that the resonance graph of an arbitrary fibonacene with n hexagons is isomorphic to the Fibonacci cube.In this paper, we consider the resonance graph of the fibonacene with n hexagons on the Möbius strips and prove that: it is isomorphic to the union of the Lucuas cubic and two isolated vertices if n is odd, and the Lucuas cubic if n is even. Futhermore, we show that the resonance graph of a class of the hexagonal chain on the Möbius strip is isomorphic to a subgraph of the hypercube and two isolated vertices. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224912 Collection 数学与统计学院 Recommended CitationGB/T 7714 赵海秀. 两类Mobius带上六角系统的共振图[D]. 兰州. 兰州大学,2016.
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