Tight distance-regular graphs and the Q-polynomial property
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,...
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oai:animorepository.dlsu.edu.ph:faculty_research-46242021-09-20T02:42:31Z Tight distance-regular graphs and the Q-polynomial property Pascasio, Arlene A. 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. 2001-01-01T08:00:00Z text text/html https://animorepository.dlsu.edu.ph/faculty_research/3622 info:doi/10.1007/s003730170063 https://animorepository.dlsu.edu.ph/context/faculty_research/article/4624/type/native/viewcontent/s003730170063.html Faculty Research Work Animo Repository Graph theory Polynomials Mathematics |
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Graph theory Polynomials Mathematics |
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Graph theory Polynomials Mathematics Pascasio, Arlene A. Tight distance-regular graphs and the Q-polynomial property |
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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. |
| format |
text |
| author |
Pascasio, Arlene A. |
| author_facet |
Pascasio, Arlene A. |
| author_sort |
Pascasio, Arlene A. |
| title |
Tight distance-regular graphs and the Q-polynomial property |
| title_short |
Tight distance-regular graphs and the Q-polynomial property |
| title_full |
Tight distance-regular graphs and the Q-polynomial property |
| title_fullStr |
Tight distance-regular graphs and the Q-polynomial property |
| title_full_unstemmed |
Tight distance-regular graphs and the Q-polynomial property |
| title_sort |
tight distance-regular graphs and the q-polynomial property |
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Animo Repository |
| publishDate |
2001 |
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https://animorepository.dlsu.edu.ph/faculty_research/3622 https://animorepository.dlsu.edu.ph/context/faculty_research/article/4624/type/native/viewcontent/s003730170063.html |
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