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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 673–685 (Mi mz8560)  

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

On Terwilliger Graphs in Which the Neighborhood of Each Vertex is Isomorphic to the Hoffman–Singleton Graph

A. L. Gavrilyuk, A. A. Makhnev

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

Abstract: The Hoffman–Singleton graph is the only strongly regular graph with parameters $(50,7,0,1)$. A well-known hypothesis states that a distance-regular graph in which the neighborhood of each vertex is isomorphic to the Hoffman–Singleton graph has intersection array $\{50,42,1;1,2,50\}$ or $\{50,42,9;1,2,42\}$. In the present paper, we prove this hypothesis under the condition that a distance-regular graph is a Terwilliger graph and the graph diameter is at most $5$.

Keywords: distance-regular graph, isomorphism, Terwilliger graph

DOI: https://doi.org/10.4213/mzm8560

Full text: PDF file (488 kB)
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English version:
Mathematical Notes, 2011, 89:5, 633–644

Bibliographic databases:

UDC: 519.17
Received: 27.11.2009

Citation: A. L. Gavrilyuk, A. A. Makhnev, “On Terwilliger Graphs in Which the Neighborhood of Each Vertex is Isomorphic to the Hoffman–Singleton Graph”, Mat. Zametki, 89:5 (2011), 673–685; Math. Notes, 89:5 (2011), 633–644

Citation in format AMSBIB
\Bibitem{GavMak11}
\by A.~L.~Gavrilyuk, A.~A.~Makhnev
\paper On Terwilliger Graphs in Which the Neighborhood of Each Vertex is Isomorphic to the Hoffman--Singleton Graph
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 5
\pages 673--685
\mathnet{http://mi.mathnet.ru/mz8560}
\crossref{https://doi.org/10.4213/mzm8560}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858556}
\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 5
\pages 633--644
\crossref{https://doi.org/10.1134/S000143461105004X}
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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. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
    2. van Dam E.R., Koolen J.H., Tanaka H., “Distance-Regular Graphs”, Electron. J. Comb., 2016, 1–156  isi
  • Математические заметки Mathematical Notes
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