An inequality for regular near polygons

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Let $G$ denote a near-polygon distance-regular graph with diameter $d\geq 3$, valency $k$ and intersection numbers $a_1>0$, $c_2>1$. Let $θ_1$ denote the second largest eigenvalue for the adjacency matrix of $G$. We show $θ_1$ is at most $(k-a_1-c_2)/(c_2-1)$. We show the following are equivalent: (i) Equality is attained above; (ii) $G$ is $Q$-polynomial with respect to $θ_1$; (iii) $G$ is a dual polar graph or a Hamming graph.
13 pages

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Combinatorics, 05E30

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http://salesiana.dossiersoluciones.com/handle/123456789/69501

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312149
 http://arxiv.org/abs/math/0312149

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arXiv