Tight distance-regular graphs and the Q-polynomial property

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Graphs and Combinatorics

Volume

17

Issue

1

First Page

149

Last Page

169

Publication Date

1-1-2001

Abstract

Let Γ denote a distance-regular graph with diameter d ≥ 3, and assume Γ is tight (in the sense of Jurišić, Koolen and Terwilliger). Let θ denote the second largest or smallest eigenvalue of Γ, and let σ0, σ1, . . . , σd denote the associated cosine sequence. We obtain an inequality involving σ0, σ1, . . . , σd for each integer i (1 ≤ i ≤ d - 1), and we show equality for all i is closely related to Γ being Q-polynomial with respect to θ. We use this idea to investigate the Q-polynomial structures in tight distance-regular graphs. © Springer-Verlag 2001.

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Digitial Object Identifier (DOI)

10.1007/s003730170063

Disciplines

Mathematics

Keywords

Graph theory; Polynomials

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