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Mat. Sb., 2000, Volume 191, Number 7, Pages 89–104 (Mi msb493)  

This article is cited in 11 scientific papers (total in 12 papers)

On graphs the neighbourhoods of whose vertices are strongly regular with $k=2\mu$

A. A. Makhnev

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

Abstract: It is proved that an amply regular graph of diameter greater than 2 the neighbourhoods of whose vertices are strongly regular with $k=2\mu$ is a Taylor graph. A description of the locally Paley graphs is obtained. Uniform extensions of the partial geometries $pG_2(4,t)$ are found.

DOI: https://doi.org/10.4213/sm493

Full text: PDF file (286 kB)
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English version:
Sbornik: Mathematics, 2000, 191:7, 1033–1048

Bibliographic databases:

UDC: 519.14
MSC: Primary 05C75; Secondary 05B25, 05E30, 51E12, 51E14
Received: 22.03.1999

Citation: A. A. Makhnev, “On graphs the neighbourhoods of whose vertices are strongly regular with $k=2\mu$”, Mat. Sb., 191:7 (2000), 89–104; Sb. Math., 191:7 (2000), 1033–1048

Citation in format AMSBIB
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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. Siberian Math. J., 43:3 (2002), 487–495  mathnet  crossref  mathscinet  isi  isi  scopus
    2. A. A. Makhnev, N. V. Chuksina, “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami $(95,40,12,20)$”, Vladikavk. matem. zhurn., 11:4 (2009), 44–58  mathnet
    3. N. V. Chuksina, “Avtomorfizmy silno regulyarnogo grafa, v kotorom okrestnosti vershin yavlyayutsya tochechnymi grafami chastichnoi geometrii $pG_2(4,9)$”, Sib. elektron. matem. izv., 6 (2009), 110–119  mathnet  mathscinet  elib
    4. K. S. Efimov, “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami $(75,32,10,16)$”, Sib. elektron. matem. izv., 7 (2010), 1–13  mathnet  mathscinet
    5. M. M. Isakova, A. A. Makhnev, “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami (64,35,18,20)”, Tr. IMM UrO RAN, 16, no. 3, 2010, 96–104  mathnet  elib
    6. A. A. Makhnev, A. A. Tokbaeva, “Ob avtomorfizmakh silno regulyarnogo grafa s parametrami (76,35,18,14)”, Tr. IMM UrO RAN, 16, no. 3, 2010, 185–194  mathnet  elib
    7. Gutnova A.K., Makhnev A.A., “On graphs in which the neighborhoods of vertices are pseudogeometric graphs for pG (s-2)(s, t)”, Doklady Mathematics, 81:2 (2010), 222–226  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. Kardanova M.L., Makhnev A.A., “On Graphs in Which the Neighborhood of Each Vertex Is the Complementary Graph of a Seidel Graph”, Doklady Mathematics, 82:2 (2010), 762–764  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. A. A. Makhnev, N. V. Chuksina, “On automorphisms of a strongly regular graph with parameters $(210,95,40,45)$”, Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 62–72  mathnet  crossref  isi  elib
    10. “Makhnev Aleksandr Alekseevich (on his 60th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), 1–11  mathnet  crossref  mathscinet
    11. A. K. Gutnova, A. A. Makhnev, “Graphs of diameter at most 3 whose local subgraphs are pseudogeometric graphs for pG s − 3(s, t)”, Dokl. Math, 91:2 (2015), 211  crossref  mathscinet  zmath  scopus  scopus  scopus
    12. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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