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On a Characterization of Bilinear Forms Graphs

✍ Scribed by K. Metsch

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 165 KB
Volume: 20
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0280

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✦ Synopsis

We show that the bilinear forms graphs H q (n, d) of diameter d ≥ 3 are characterized as distanceregular graphs by their parameters provided that either n ≥ d + 3 and q ≥ 3, or n ≥ d + 4 and q = 2. As a corollary of the method used, we can show the following. If is a distance-regular graph with classical parameters (d, q, α, β) and diameter d ≥ 3, then either is a Johnson graph, a Grassmann graph, a Hamming graph, or a bilinear forms graph, or β is bounded in terms of d, q and α.

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