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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 3, Pages 35–42 (Mi vmj588)  

This article is cited in 2 scientific papers (total in 2 papers)

Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$

A. K. Gutnovaa, A. A. Makhnevb

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue $\leq t$ for a given positive integer $t$. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with non-principal eigenvalue $t$ for $t=1,2,…$ In the article by A. K. Gutnova and A. A. Makhnev “Extensions of pseudogeometrical graphs for $pG_{s-4}(s,t)$” the Koolen problem was solved for $t=4$ and for pseudogeometrical neighborhoods of vertices. In the article of A. A. Makhnev “Strongly regular graphs with nonprincipal eigenvalue 5 and its extensions” the Koolen problem for $t=5$ was reduced to the case where the neighborhoods of vertices are exceptional graphs. In this paper intersection arrays for distance-regular graphs whose local subgraphs are exceptional pseudogeometric graphs for $pG_{s-5}(s,t)$.

Key words: distance-regular graph, pseudogeometric graph, eigenvalue of graph.

Funding Agency Grant Number
Russian Science Foundation 15-11-10025
Ministry of Education and Science of the Russian Federation 02.A03.21.0006


Full text: PDF file (215 kB)
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UDC: 519.17
Received: 18.02.2016

Citation: A. K. Gutnova, A. A. Makhnev, “Extensions of pseudogeometric graphs for $pG_{s-5}(s,t)$”, Vladikavkaz. Mat. Zh., 18:3 (2016), 35–42

Citation in format AMSBIB
\Bibitem{GutMak16}
\by A.~K.~Gutnova, A.~A.~Makhnev
\paper Extensions of pseudogeometric graphs for~$pG_{s-5}(s,t)$
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 3
\pages 35--42
\mathnet{http://mi.mathnet.ru/vmj588}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Makhnev, D. V. Paduchikh, “Grafy, v kotorykh lokalnye podgrafy silno regulyarny so vtorym sobstvennym znacheniem 5”, Tr. IMM UrO RAN, 22, no. 4, 2016, 188–200  mathnet  crossref  mathscinet  elib
    2. A. K. Gutnova, V. V. Bitkina, “Distantsionno regulyarnye lokalno $pG_{s-6}(s,t)$-grafy diametra, bolshego $3$”, Tr. IMM UrO RAN, 24, no. 3, 2018, 34–42  mathnet  crossref  elib
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