Title: An inequality for regular near polygons
Authors: Terwilliger, P
Weng, CW
Department of Applied Mathematics
Keywords: near polygon;distance-regular graph;Q-polynomial;dual polar graph;Hamming graph
Issue Date: 1-Feb-2005
Abstract: Let Gamma denote a near polygon distance-regular graph with diameter d greater than or equal to 3, valency k and intersection numbers a(1) > 0, c(2) > 1. Let theta(1) denote the second largest eigenvalue of Gamma. We show theta(1) less than or equal to k - a(1) - c(2)/ c(2) - 1. We show the following (i)-(iii) are equivalent. (i) Equality is attained above; (ii) Gamma is Q-polynomial with respect to theta(1); (iii) Gamma is a dual polar graph or a Hamming graph. (C) 2004 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.ejc.2004.03.001
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.03.001
Volume: 26
Issue: 2
Begin Page: 227
End Page: 235
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