On Shilla Graphs Γ With b2=c2 Having Eigenvalue θ2=0
- Authors: Makhnev A.A.1, Bitkina V.V.2, Gutnova A.K.2
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Affiliations:
- Institute of Mathematics and Mechanics named after A.I. N.N. Krasovsky, Ural Branch of the Russian Academy of Sciences
- North Ossetian State University after K.L. Khetagurov
- Issue: No 3 (66) (2024)
- Pages: 16-22
- Section: Mathematics
- URL: https://journal-vniispk.ru/1993-0550/article/view/307279
- DOI: https://doi.org/10.17072/1993-0550-2024-3-16-22
- ID: 307279
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Abstract
The Shilla graph with b2=c2 and eigenvalue θ2=0 has intersection array {b(b+1)s,(bs+s+1)(b-1),bs;1,bs,(b2-1)s}. There are only seven graphs out of 55 with b<100 do not lie in the series {4s3+6s2+2s,4s3+4s2+2s,2s2+s;1,2s2+s,4s3+4s2}.
This paper studies the Shilla graphs with b2=c2, eigenvalue θ2=0 and intersection array.
Keywords
About the authors
A. A. Makhnev
Institute of Mathematics and Mechanics named after A.I. N.N. Krasovsky, Ural Branch of the Russian Academy of Sciences
Author for correspondence.
Email: makhnev@imm.uran.ru
Doctor of Physical and Mathematical Sciences, Professor, Corresponding Member of the Russian Academy of Sciences, Laureate of the A.I. Maltsev Prize, Chief Researcher 16 S. Kovalevskaya St., Yekaterinburg, Russia, 620990
V. V. Bitkina
North Ossetian State University after K.L. Khetagurov
Email: viktoriya.v@mail.ru
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Applied Mathematics and Informatics 44-46 Vatutina St., Vladikavkaz, Russia, 362025
A. K. Gutnova
North Ossetian State University after K.L. Khetagurov
Email: gutnovaalina@gmail.com
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Applied Mathematics and Informatics 44-46 Vatutina St., Vladikavkaz, Russia, 362025
References
- Brouwer, A.E., Cohen, A.N. and Neumaier, A. (1989), "Distance-Regular Graphs", Springer-Verlag. Berlin Heidelberg New-York.
- Koolen, J. and Park, J. (2010), "Shilla distance-regular graphs", Europ. J. Comb, 31, pp. 2064-2073.
- Makhnev, A.A. and Belousov, I.N. (2022), "On distance-regular graphs of diameter 3 with eigenvalue", Trudy Institute Math. (Novosibirsk), 33, no. 1, pp. 162-173.
- Coolsaet, K. and Juriˇsi´c, A. (2008), "Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs", J. Comb. Theory, Series A, vol. 115, pp. 1086-1095.
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