A characterization of some distance-regular graphs by strongly closed subgraphs
A characterization of some distance-regular graphs by strongly closed subgraphs
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DOI：
10.1016/j.ejc.2008.07.015
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发表时间：
2009-05
期刊：
影响因子：
--
通讯作者：
Akira Hiraki
中科院分区：
文献类型：
--
作者：
Akira Hiraki
本文研究了一个直径d≥4的距离正则图Γ，使得对于任意给定的距离为d−1的顶点对，存在一个包含它们的直径为d−1的强闭子图.证明了关于Γ的交数的几个不等式。我们证明了，如果某些不等式中的等式成立，则Γ是奇图、双奇图、双Grassmann图、Hamming图或对偶极图.
In this paper we study a distance-regular graph Γ of diameter d≥4 such that for any given pair of vertices at distance d−1 there exists a strongly closed subgraph of diameter d−1 containing them. We prove several inequalities for intersection numbers of Γ. We show that if the equalities hold in some of these inequalities, then Γ is either the Odd graph, the doubled Odd graph, the doubled Grassmann graph, the Hamming graph or the dual polar graph.