Shilla distance-regular graphs
Shilla distance-regular graphs
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DOI：
10.1016/j.ejc.2010.05.012
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发表时间：
2009-02
期刊：
影响因子：
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通讯作者：
J. Koolen;Jongyook Park
中科院分区：
文献类型：
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作者：
J. Koolen;Jongyook Park
一个Shilla距离正则图Γ（比如说k度）是一个直径为3的距离正则图，使得它的第二大特征值等于a3。我们将证明对于Shilla距离正则图Γ，a3可除k，对于Γ，我们定义B=B（Γ）ka3。本文证明了存在1000个固定B（Γ）≥2的Shilla距离正则图Γ.此外，我们还对B（Γ）=2和B（Γ）=3的Shilla距离正则图进行了分类.此外，我们将给出一个新的距离正则图的存在性条件。
A Shilla distance-regular graph Γ (say with valency k) is a distance-regular graph with diameter 3 such that its second-largest eigenvalue equals a3. We will show that a3divides k for a Shilla distance-regular graph Γ, and for Γ we define b=b(Γ)≔ka3. In this paper we will show that there are finitely many Shilla distance-regular graphs Γ with fixed b(Γ)≥2. Also, we will classify Shilla distance-regular graphs with b(Γ)=2 and b(Γ)=3. Furthermore, we will give a new existence condition for distance-regular graphs, in general.