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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 4, Pages 188–200
DOI: https://doi.org/10.21538/0134-4889-2016-22-4-188-200 (Mi timm1365) 		 
Graphs in which local subgraphs are strongly regular with second eigenvalue 5

A. A. Makhnevab, D. V. Paduchikha

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2016-22-4-188-200
Abstract: J. Koolen proposed the problem of studying distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs with second eigenvalue $\le t$ for a given positive integer $t$. Earlier Koolen's problem was solved for $t=4$. We complete the classification of distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs with second eigenvalue $r$, where $4$<$r\le5$.
Keywords: strongly regular graph, eigenvalue, distance-regular graph.
Funding agency Grant number
Russian Science Foundation 14-11-00061
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Received: 18.08.2016
Bibliographic databases:
Document Type: Article
UDC: 519.17
MSC: 05B25, 05C25
Language: Russian
Citation: A. A. Makhnev, D. V. Paduchikh, “Graphs in which local subgraphs are strongly regular with second eigenvalue 5”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 4, 2016, 188–200
Citation in format AMSBIB
\Bibitem{MakPad16}
\by A.~A.~Makhnev, D.~V.~Paduchikh
\paper Graphs in which local subgraphs are strongly regular with second eigenvalue 5
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 4
\pages 188--200
\mathnet{http://mi.mathnet.ru/timm1365}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-4-188-200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3590933}
\elib{https://elibrary.ru/item.asp?id=27350137}
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