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On distance-regular graphs with fixed valency

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Abstract

We prove the following result. LetΓ be a finite distance-regular graph. Letc i ,a i ,b i be the intersection numbers ofΓ. IfΓ is not an ordinaryn-gon, then the number of (c i ,a i ,b i ) such thatc i =b i is bounded by a certain function of the valencyk, say 10k2 k.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queen Mary College, E1 4NS, London, U.K.

    Eiichi Bannai & Tatsuro Ito

  2. Department of Mathematics, Joetsu University of Education, 943, Joetsu, Niigata, Japan

    Eiichi Bannai & Tatsuro Ito

  3. Department of Mathematics, Ohio State University, 43210, Columbus, OH, USA

    Eiichi Bannai & Tatsuro Ito

Authors
  1. Eiichi Bannai
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  2. Tatsuro Ito
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Additional information

Dedicated to Professor Hirosi Nagao on his 60th birthday

Supported in part by N.S.F. grant MCS-830826. Also supported by Senior Visiting Scientist Grant of the British S.E.R.C. GR/C/97491 to visit Q.M.C. (University of London) 1984/5.

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Bannai, E., Ito, T. On distance-regular graphs with fixed valency. Graphs and Combinatorics 3, 95–109 (1987). https://doi.org/10.1007/BF01788534

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  • DOI: https://doi.org/10.1007/BF01788534

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