The classification of distance-regular graphs of type IIB

Abstract

The distance-regular graphsΛ of type IIB in Bannai and Ito [1] have intersection numbers of the form

whered is the diameter of Λ, andh, x, andt are complex constants. In this paper we show a graph of type IIB and diameterd (3≦d) is either the antipodal quotient of the Hamming graphH(2d+1,2), or has the same intersection numbers as the antipodal quotient ofH(2d, 2).

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Terwilliger, P. The classification of distance-regular graphs of type IIB. Combinatorica 8, 125–132 (1988). https://doi.org/10.1007/BF02122560

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AMS subject classification

  • 05 C 50
  • 05 C 75