兰州大学机构库 >数学与统计学院
关于一些图类的匹配强迫数及谱的研究
Alternative TitleStudy on the forcing matching number and spectra of some classes of graphs
蒋晓艳
Thesis Advisor张和平
2011-06-03
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword强迫数 强迫谱 匹配可交换 硼氮富勒烯图 偶多边形链 六角系统 Z-变换图
Abstract设G是一个有完美匹配的图. 若G的完美匹配M的子集S只包含在唯一完美匹配M中,则称S是M的一个强迫集。完美匹配M的最小强迫集的大小称作M的强迫数,记作f(G,M) 。在图G的所有完美匹配中,强迫数的最小(大)值叫做G的最小(大)强迫数。图G的所有完美匹配的强迫数构成的集合叫做G的强迫谱. 本文主要研究了一些图类的强迫数或强迫谱。我们给出了环边连通度为3的硼氮富勒烯图的强迫谱,刻画了达到下界2的环边连通度为4的硼氮富勒烯图,得到了三类图的最大强迫数,证明了任偶多边形链的强迫谱是连续的, 探讨了两类cata-型六角系统的强迫谱的连续性。
Other AbstractLet G be a graph with perfect matchings. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matchings of G. The smallest cardinality of forcing sets of M is called the forcing number of M, denoted by f(G;M). The minimum (resp. maximum) forcing number of G is the minimum (resp. maximum) value of forcing numbers of all perfect matchings of G. The forcing spectrum of G is the set of all matching forcing numbers of G. In this thesis, we mainly study the matching forcing number and forcing spectrum of some classes of graphs. We obtain the forcing spectrum of boron-nitrogen fullerene graphs with cyclic edge-connectivity 3, determine all boron-nitrogen fullerene graphs with cyclic edge-connectivity 4 whose minimum forcing number arrive in the lower bound 2, give the maximum forcing number of three classes of graphs, prove that the forcing spectrum of any even polygonal chain is continuous, investigate the continuity of forcing spectrum of two classes of cata-condensed hexagonal system.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225326
Collection数学与统计学院
Recommended Citation
GB/T 7714
蒋晓艳. 关于一些图类的匹配强迫数及谱的研究[D]. 兰州. 兰州大学,2011.
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