兰州大学机构库 >数学与统计学院
半凯莱图的匹配可扩性及其应用
Alternative TitleOn the extendability of semi-Cayley graph and it's applications
刘文文
Thesis Advisor张和平
2009-06-02
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword半凯莱图 凯莱图 二面体群 广义双循环群 匹配可扩
Abstract半凯莱图是这样的一个图: 它的自同构群是半正则的并且有两个大小相等的轨道. 对至少有2n+2个顶点的连通图~$\Gamma$, 若图~$\Gamma$ 的每一个大小为n的匹配可以扩充为~$\Gamma$ 的一个完美匹配,则~$\Gamma$ 为n可扩的. 本文主要刻画了有限阿贝尔群上的半凯莱图~$SC(G;A,B,C)$ 的1- 可扩性和2- 可扩性, 其中集合A 和B是相同的. 用本文的结果我们分别刻画了二面体群和广义双循环群上的凯莱图的2- 可扩性. 我们还证明了有限阿贝尔群上的半凯莱图包括偶数阶的有限阿贝尔群上的 凯莱图.
Other AbstractA semi-Cayley graph is a graph which admits a semiregular automorphism group with two orbits of equal size. A connected graph $\Gamma$ with at least 2n+2 vertices is said to be n-extendable if every matching of size $n$ in $\Gamma$ can be extended to a perfect matching. The aim of this paper is to study the 1-extendable and 2-extendable semi-Cayley graphs $SC(G;A,B,C)$ over finite abelian groups with the additional condition that A=B.As applications, the $2$-extendable Cayley graphs over dihedral groups and generalized dicyclic groups are classified, respectively. We also prove that semi-Cayley graphs over finite abelian groupscontains Cayleygraphs over finite abelian groups with even order.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225631
Collection数学与统计学院
Recommended Citation
GB/T 7714
刘文文. 半凯莱图的匹配可扩性及其应用[D]. 兰州. 兰州大学,2009.
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