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On Distance-Regular Graphs with Height Two, II
Authors:Masato Tomiyama
Institution:(1) Division of Mathematical Science, Osaka Kyoiku University, Asahigaoka 4-698-1, Kashiwara, Osaka, 582, Japan
Abstract:Let Gamma be a distance-regular graph with diameter 
$$d \geqslant 3 $$
and height 
$$h = 2 $$
, where 
$$h = max\{ i:p_{d,i}^d \ne 0\} $$
. Suppose that for every agr in Gamma and every beta in 
$$\Gamma _d (\alpha ) $$
, the induced subgraph on 
$$\Gamma _d (\alpha ) \cap \Gamma _2 (\beta ) $$
is isomorphic to a complete multipartite graph 
$$K_{t \times 2} $$
with 
$$t \geqslant 2 $$
. Then 
$$d = 4 $$
and Gamma is isomorphic to the Johnson graph 
$$\begin{gathered} J(10,4) \hfill \\ \hfill \\ \end{gathered} $$
.
Keywords:distance-regular graph  height  Johnson graph  complete multipartite graph
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