Symplectic graphs over finite local rings
Symplectic graphs over finite local rings
复制标题
DOI：
10.1016/j.ejc.2013.03.003
复制
发表时间：
2013-10
期刊：
影响因子：
--
通讯作者：
Yotsanan Meemark;Thammanoon Puirod
中科院分区：
文献类型：
--
作者：
Yotsanan Meemark;Thammanoon Puirod
这项工作是基于Meemark和Prinyasart（2011）[8]的思想，他们引入了辛图[公式：见正文]，其中V是有限交换环R上的辛空间。当[公式：[见正文]和V=R2v，他们证明了[公式：见正文]当ν=1时是强正则图，Li，Wang和Guo（2012）[6]证明了当ν≥2时是严格Deza图。本文研究了有限局部环上的辛图。如果我们的图是强正则图或严格Deza图，我们可以分类。我们还证明了它是弧传递的。此外，我们应用Meemark和Prinyasart（2011）[8]中提出的组合技术来证明辛图的子成分上的类似结果。
This work is based on ideas of Meemark and Prinyasart (2011) [8] who introduced the symplectic graph [Formula: see text] , where V is a symplectic space over a finite commutative ring R. When [Formula: see text] and V=R2v, they proved that [Formula: see text] is an strongly regular graph when ν=1 and Li, Wang and Guo (2012) [6] showed that it is a strictly Deza graph when ν≥2. In this paper, we study symplectic graphs over finite local rings. We can classify if our graph is a strongly regular graph or a strictly Deza graph. We also show that it is arc transitive. Moreover, we apply the combinatorial technique presented in Meemark and Prinyasart (2011) [8] to prove similar results on subconstituents of symplectic graphs.