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Mat. Zametki, 2007, Volume 82, Issue 1, Pages 14–26 (Mi mz3749)  

This article is cited in 5 scientific papers (total in 6 papers)

Terwilliger Graphs with $\mu\le3$

A. L. Gavrilyuk, A. A. Makhnev

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

Abstract: A Terwilliger graph is a noncomplete graph in which intersection of the neighborhoods of any two vertices at distance 2 from each other is a $\mu$-clique. We classify connected Terwilliger graphs with $\mu=3$ and describe the structure of Terwilliger graphs of diameter 2 with $\mu=2$.

Keywords: undirected graph, regular graph, biregular graph, Terwilliger graph, edge regular graph, clique extension, Fibonacci number, affine and projective plane

DOI: https://doi.org/10.4213/mzm3749

Full text: PDF file (484 kB)
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English version:
Mathematical Notes, 2007, 82:1, 13–24

Bibliographic databases:

UDC: 519.14
Received: 22.05.2006

Citation: A. L. Gavrilyuk, A. A. Makhnev, “Terwilliger Graphs with $\mu\le3$”, Mat. Zametki, 82:1 (2007), 14–26; Math. Notes, 82:1 (2007), 13–24

Citation in format AMSBIB
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\paper Terwilliger Graphs with $\mu\le3$
\jour Mat. Zametki
\yr 2007
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\pages 14--26
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Gavrilyuk, “Ob izospektralnykh podgrafakh biregulyarnykh geodezicheskikh grafov diametra 2”, Tr. IMM UrO RAN, 13, no. 4, 2007, 49–60  mathnet  elib
    2. A. L. Gavrilyuk, A. A. Makhnev, “Terwilliger graphs in which the neighborhood of some vertex is isomorphic to a Petersen graph”, Doklady Mathematics, 78:1 (2008), 550–553  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. A. L. Gavrilyuk, A. A. Makhnev, “Geodesic Graphs with Homogeneity Conditions”, Doklady Mathematics, 78:2 (2008), 743  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. A. L. Gavrilyuk, “On Terwilliger graphs with $\mu=4$”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S90–S99  mathnet  crossref  isi  elib
    5. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
    6. Gutnova A.K., Makhnev A.A., “on Graphs Whose Local Subgraphs Are Pseudogeometric For Gq(4, T)”, Dokl. Math., 91:3 (2015), 371–375  crossref  mathscinet  zmath  isi  elib  scopus
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