Abstract
The Hamming graph H ( d , q ) satisfies the following conditions: (i) For any pair ( u , v ) of vertices there exists a strongly closed subgraph containing them whose diameter is the distance between u and v . In particular, any strongly closed subgraph is distance-regular. (ii) For any pair ( x , y ) of vertices at distance d − 1 the subgraph induced by the neighbors of y at distance d from x is a clique of size a 1 + 1 . In this paper we prove that a distance-regular graph which satisfies these conditions is a Hamming graph.
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