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On Distance-Regular Graphs with Height Two
Authors:Masato Tomiyama
Institution:(1) Graduate School of Mathematics, Kyushu University, Higashi-ku, Fukuoka, 812, Japan
Abstract:Let Gamma be a distance-regular graph with diameter at least three and height h = 2, where 
$$\max \left\{ {i:p_{di}^d \ne 0} \right\}$$
. Suppose that for every agr in Gamma and beta in Gammad(agr), the induced subgraph on Gammad(agr) cap Gamma2(beta) is a clique. Then Gamma is isomorphic to the Johnson graph J(8, 3).
Keywords:distance-regular graph  strongly regular graph  height  clique  Johnson graph
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