Arc-transitive distance-regular covers of cliques with λ = μ

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• 作者：A. A. Makhnev (1) (2)
  D. V. Paduchikh (1)
  L. Yu. Tsiovkina (1)
  
• 关键词：arc ; transitive graphs ; antipodal distance ; regular graphs ; automorphism groups
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：284
• 期：1-supp
• 页码：124-134
• 全文大小：1,332 KB
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• 作者单位：A. A. Makhnev (1) (2)
  D. V. Paduchikh (1)
  L. Yu. Tsiovkina (1)
  
  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia
  2. Institute of Radioelectronics and Informational Technologies, Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russia
  
• ISSN：1531-8605

文摘

We study antipodal distance-regular graphs of diameter 3 such that their automorphism group acts transitively on the set of pairs (a, b), where {a, b} is an edge of the graph. Since the automorphism group of such graphs acts 2-transitively on the set of antipodal classes, the classification of 2-transitive permutation groups can be used. We classify arc-transitive distance-regular graphs of diameter 3 in which any two vertices at distance at most two have exactly μ common neighbors.