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On distance-regular graphs with fixed valency, II

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Abstract

LetГ be a distance-regular graph of valencyk ≥ 3 and diameterd. Suppose the intersection array hast columns different fromt(1, 0,k − 1). Then it is shown thatd is bounded from above by a certain functionf(k, t) depending only onk andt. As an application, this theorem eliminates certain cubic distance-regular graphs to complete the classification of such graphs by Biggs et al.

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Authors and Affiliations

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

    Eiichi Bannai

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

    Tatsuro Ito

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

    Eiichi Bannai

Authors
  1. Eiichi Bannai
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  2. Tatsuro Ito
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Supported in part by NSF grant MCS-8301826 and by the British SERC grant.

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Bannai, E., Ito, T. On distance-regular graphs with fixed valency, II. Graphs and Combinatorics 4, 219–228 (1988). https://doi.org/10.1007/BF01864162

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  • DOI: https://doi.org/10.1007/BF01864162

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