当前位置: X-MOL 学术J. Comb. Theory B › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2020-12-16 , DOI: 10.1016/j.jctb.2020.12.001
Binzhou Xia

Half-arc-transitive graphs are a fascinating topic which connects graph theory, Riemann surfaces and group theory. Although fruitful results have been obtained over the last half a century, it is still challenging to construct half-arc-transitive graphs with prescribed vertex stabilizers. Until recently, there have been only six known connected tetravalent half-arc-transitive graphs with nonabelian vertex stabilizers, and the question whether there exists a connected tetravalent half-arc-transitive graph with nonabelian vertex stabilizer of order 2s for every s3 has been wide open. This question is answered in the affirmative in this paper via the construction of a connected tetravalent half-arc-transitive graph with vertex stabilizer D82×C2m for each integer m1, where D82 is the direct product of two copies of the dihedral group of order 8 and C2m is the direct product of m copies of the cyclic group of order 2. The graphs constructed have surprisingly many significant properties in various contexts.



中文翻译:

具有无界nonabelian顶点稳定器的四价半弧传递图

半弧传递图是连接图论,黎曼曲面和群论的一个引人入胜的话题。尽管在过去的半个世纪中取得了丰硕的成果,但使用规定的顶点稳定器构造半弧传递图仍然具有挑战性。直到最近,只有六个已知的带有非阿贝尔顶点稳定剂的连接的四价半弧-传递图,以及是否存在一个带非阿贝尔顶点稳定剂的连接的四价半弧-传递图的问题2s 每一个 s3已经敞开了。通过建立带有顶点稳定器的连接的四价半弧-传递图的连接,该问题得到了肯定的回答。d82×C2 对于每个整数 1个,在哪里 d82 是8阶二面体组的两个副本的直接乘积, C2是2阶环状基团的m个副本的直接乘积。在各种情况下,构造的图都具有令人惊讶的许多重要特性。

更新日期:2020-12-16
down
wechat
bug