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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 143–161 (Mi timm231)  

This article is cited in 1 scientific paper (total in 2 paper)

Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph

A. A. Makhnev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Connected graphs are studied in which neighborhoods of vertices are isomorphic to the Hoffman—Singleton graph (i.e., the strongly regular graph with parameters (50,7,0,1)). It is proved that a distance-regular graph in which neighborhoods of vertices are isomorphic to the Hoffman—Singleton graph has $\mu=2$.

Keywords: Hoffman-Singleton graph, distance-regular graph, locally $\mathcal F$-graph

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S128–S148

Bibliographic databases:

UDC: 519.17
Received: 24.11.2008

Citation: A. A. Makhnev, “Graphs in which neighborhoods of vertices are isomorphic to the Hoffman–Singleton graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 143–161; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S128–S148

Citation in format AMSBIB
\Bibitem{Mak09}
\by A.~A.~Makhnev
\paper Graphs in which neighborhoods of vertices are isomorphic to the Hoffman--Singleton graph
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 143--161
\mathnet{http://mi.mathnet.ru/timm231}
\elib{http://elibrary.ru/item.asp?id=12878777}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S128--S148
\crossref{https://doi.org/10.1134/S008154380907013X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900013}


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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. L. Gavrilyuk, A. A. Makhnev, “On Terwilliger Graphs in Which the Neighborhood of Each Vertex is Isomorphic to the Hoffman–Singleton Graph”, Math. Notes, 89:5 (2011), 633–644  mathnet  crossref  crossref  mathscinet  isi
    2. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
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