Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with \(\lambda =\mu \) related to groups 详细信息    查看全文

• 作者：L. Yu. Tsiovkina
• 关键词：Antipodal graph ; Arc ; transitive graph ; Automorphism group ; Distance ; regular graph ; $$r$$ r ; Fold covering graph ; 05E18 ; 05E30
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：41
• 期：4
• 页码：1079-1087
• 全文大小：386 KB
• 参考文献：1.Aschbacher, M.: Finite Group Theory, 2nd edn. Cambridge University Press, Cambridge (2000)View Article MATH
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  5.Godsil, C.D., Liebler, R.A., Praeger, C.E.: Antipodal distance transitive covers of complete graphs. Eur. J. Comb. 19(4), 455鈥?78 (1998)View Article MATH MathSciNet
  6.Klin, M., Pech, Ch.: A new construction of antipodal distance-regular covers of complete graphs through the use of Godsil-Hensel matrices. ARS Math. Contemp. 4, 205鈥?43 (2011)MATH MathSciNet
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  8.Makhnev, A.A., Paduchikh, D.V., Tsiovkina, L.Yu.: Arc-transitive distance-regular covers of cliques with \(\lambda =\mu \) . Proc. Steklov Inst. Math. 284(Suppl. 1), 124鈥?34 (2014)
  9.Suzuki, M.: On a class of doubly transitive groups. Ann. Math. Second Ser. 75(1), 105鈥?45 (1962)View Article MATH
  10.Suzuki, M.: Finite groups of even order in which Sylow 2-groups are independent. Ann. Math. Second Ser. 80(1), 58鈥?7 (1964)View Article MATH
  11.Ward, H.N.: On Ree鈥檚 series of simple groups. Trans. Am. Math. Soc. 121(1), 62鈥?9 (1966)MATH
  12.van Dam, E.R., Koolen, J.H., Tanaka, H.: Distance-Regular Graphs, manuscript.https://鈥媠ites.鈥媑oogle.鈥媍om/鈥媠ite/鈥媏dwinrvandam/鈥媝ub (2014). Accessed 9 July 2014
  
• 作者单位：L. Yu. Tsiovkina (1)
  
  1. Department of Algebra and Topology, Krasovsky Institute of Mathematics and Mechanics of UB RAS, 16, S.Kovalevskaya street, Yekaterinburg, 620990, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Convex and Discrete Geometry
  Order, Lattices and Ordered Algebraic Structures
  Computer Science, general
  Group Theory and Generalizations
  
• 出版者：Springer U.S.
• ISSN：1572-9192

文摘

In this paper, we construct two new infinite families of arc-transitive distance-regular graphs, related to Suzuki groups \(Sz(q)\) and Ree groups \(^2G_2(q)\), where \(q>3\). They are antipodal \(r\)-covers of complete graphs on \(q^2+1\) or \(q^3+1\) vertices, respectively, with \(\lambda =\mu \) and \(r>1\) being an arbitrary odd divisor of \(q-1\). We also find that the graph on the set of involutions of \(Sz(q)\) with \(q>3\), whose edges are the pairs of involutions \(\{u,v\}\) such that \(|uv|=5\), is distance-regular.