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Ural Mathematical Journal, 2021, Volume 7, Issue 2, Pages 51–58
DOI: https://doi.org/10.15826/umj.2021.2.004 (Mi umj149) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Shilla graphs with $b = 5$ and $b = 6$

Alexander A. Makhnevab, Ivan N. Belousovba

a Ural Federal University
b Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (121 kB) Citations (3)
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DOI: https://doi.org/10.15826/umj.2021.2.004
Abstract: A $Q$-polynomial Shilla graph with ${b = 5}$ has intersection arrays ${\{105t,4(21t+1),16(t+1);}$ ${1,4 (t+1),84t\}}$, $t\in\{3,4,19\}$. The paper proves that distance-regular graphs with these intersection arrays do not exist. Moreover, feasible intersection arrays of $Q$-polynomial Shilla graphs with $b = 6$ are found.
Keywords: Shilla graph, distance-regular graph, $Q$-polynomial graph.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-53013
This work was supported by RFBR and NSFC (project № 20-51-53013).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Alexander A. Makhnev, Ivan N. Belousov, “Shilla graphs with $b = 5$ and $b = 6$”, Ural Math. J., 7:2 (2021), 51–58
Citation in format AMSBIB
\Bibitem{MakBel21}
\by Alexander~A.~Makhnev, Ivan~N.~Belousov
\paper Shilla graphs with $b = 5$ and $b = 6$
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 2
\pages 51--58
\mathnet{http://mi.mathnet.ru/umj149}
\crossref{https://doi.org/10.15826/umj.2021.2.004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4358913}
\elib{https://elibrary.ru/item.asp?id=47556641}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124288794}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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