On Shilla Graphs Γ With b2=c2 Having Eigenvalue θ2=0
DOI:
https://doi.org/10.17072/1993-0550-2024-3-16-22Keywords:
block scheme, distance-regular graph, Shilla graphAbstract
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 {4s3+6s2+2s,4s3+4s2+2s,2s2+s;1,2s2+s,4s3+4s2}.References
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Koolen J, Park J. Shilla distance-regular graphs // Europ. J. Comb. 31, 2064–2073, 2010.
Makhnev A.A., Belousov I.N. On distance-regular graphs of diameter 3 with eigenvalue // Trudy Institute Math. (Novosibirsk). 33, № 1, 162–173, 2022.
Coolsaet K., Juriˇsi´c A. Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs // J. Comb. Theory, Series A. 2008. Vol. 115. 1086–1095.
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Copyright (c) 2024 Александр Алексеевич Махнев, Виктория Васильевна Биткина, Алина Казбековна Гутнова
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles are published under license Creative Commons Attribution 4.0 International (CC BY 4.0).
