An inequality for regular near polygons

Paul Terwilliger; Chih-wen Weng

doi:10.1016/j.ejc.2004.03.001

An inequality for regular near polygons

Paul Terwilliger^*, Chih-wen Weng

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摘要

Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a₁ > 0, c₂ > 1. Let θ₁ denote the second largest eigenvalue of Γ. We show θ₁≤k-a₁-c₂/c₂-1. We show the following (i)-(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ₁; (iii) Γ is a dual polar graph or a Hamming graph.

原文	English
頁（從 - 到）	227-235
頁數	9
期刊	European Journal of Combinatorics
卷	26
發行號	2
DOIs	https://doi.org/10.1016/j.ejc.2004.03.001
出版狀態	Published - 2月 2005

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10.1016/j.ejc.2004.03.001

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AU - Weng, Chih-wen

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N2 - Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a1 > 0, c2 > 1. Let θ1 denote the second largest eigenvalue of Γ. We show θ1≤k-a1-c2/c2-1. We show the following (i)-(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ1; (iii) Γ is a dual polar graph or a Hamming graph.

AB - Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a1 > 0, c2 > 1. Let θ1 denote the second largest eigenvalue of Γ. We show θ1≤k-a1-c2/c2-1. We show the following (i)-(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ1; (iii) Γ is a dual polar graph or a Hamming graph.

KW - Distance-regular graph

KW - Dual polar graph

KW - Hamming graph

KW - Near polygon

KW - Q-polynomial

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JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

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ER -

An inequality for regular near polygons

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