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The classification of distance-regular graphs of type IIB. (English) Zbl 0727.05050
Summary: The distance-regular graphs $$\Gamma$$ of type IIB in [E. Bannai and T. Ito, Algebraic combinatorics. I: Association schemes (1984; Zbl 0555.05019)] have intersection numbers of the form $k=-hxd(t-1)^{-1}$ $b_ i=h(i-t)(i-x)(i-d)(2i-t)^{-1}(2i-t+1)^{-1}(1\leq i\leq d-1)$ $c_ i=-hi(i-t+x)(i-t+d)(2i-t)^{-1}(2i-t-1)^{-1}(1\leq i\leq d-1)$ $c_ d=-hd(d-t+x)(2d-t-1)^{-1},$ where d is the diameter of $$\Gamma$$, and h,x, and t are complex constants. In this paper we show a graph of type IIB and diameter d(3$$\leq d)$$ is either the antipoldal quotient of the Hamming graph $$H(2d+1,2)$$, or has the same intersection numbers as the antipodal quotient of H(2d,2).

##### MSC:
 05C75 Structural characterization of families of graphs 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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##### References:
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