A characterization of the Hamming graph by strongly closed subgraphs

Authors:
Akira Hiraki
Affiliations:
Division of Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
Venue:
European Journal of Combinatorics
Year:
2008

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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.