An inequality for regular near polygons

Details An inequality for regular near polygons An inequality for regular near polygons

2003-12-07

arxiv.org/abs/math/0312149v1

Mathematics

Combinatorics

13 pages

Scientific paper

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 $\theta_1$ denote the second largest eigenvalue for the adjacency matrix of $G$. We show $\theta_1$ 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 $\theta_1$; (iii) $G$ is a dual polar graph or a Hamming graph.

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