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Antipodal distance-regular graphs of diameter four and five

✍ Scribed by Tilla Schade

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 179 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:1<69::aid-jcd8>3.0.co;2-v

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✦ Synopsis

An antipodal distance-regular graph of diameter four or five is a covering graph of a connected strongly regular graph. We give existence conditions for these graphs and show for some types of strongly regular graphs that no nontrivial covers exist.

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✍ Fiol, M. A.; Garriga, E.; Yebra, J. L. A. 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 383 KB 👁 2 views

Let Γ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (λ) > n -1, then D ≤ d -1, where P is the polynomial of degree d-1 which takes alternating values ±1 at λ 1 , . . . , λ d . The graphs satisfying P (λ) = n -1, called boundary graphs, h