Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 4, Pages 753–768 (Mi smj892)  

This article is cited in 4 scientific papers (total in 5 papers)

Amply regular graphs and block designs

A. L. Gavrilyuk, A. A. Makhnev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (259 kB) Citations (5)
References:
Abstract: We study the amply regular diameter $d$ graphs $\Gamma$ such that for some vertex $a$ the set of vertices at distance $d$ from $a$ is the set of points of a 2-design whose set of blocks consists of the intersections of the neighborhoods of points with the set of vertices at distance $d-1$ from $a$. We prove that the subgraph induced by the set of points is a clique, a coclique, or a strongly regular diameter 2 graph. For diameter 3 graphs we establish that this construction is a 2-design for each vertex $a$ if and only if the graph is distance-regular and for each vertex $a$ the subgraph $\Gamma_3(a)$ is a clique, a coclique, or a strongly regular graph. We obtain the list of admissible parameters for designs and diameter 3 graphs under the assumption that the subgraph induced by the set of points is a Seidel graph. We show that some of the parameters found cannot correspond to distance-regular graphs.
Keywords: amply regular graph, $t-(v,k,\lambda)$-design, strongly regular graph.
Received: 12.05.2004
Revised: 30.12.2005
English version:
Siberian Mathematical Journal, 2006, Volume 47, Issue 4, Pages 621–633
DOI: https://doi.org/10.1007/s11202-006-0073-y
Bibliographic databases:
UDC: 519.14
Language: Russian
Citation: A. L. Gavrilyuk, A. A. Makhnev, “Amply regular graphs and block designs”, Sibirsk. Mat. Zh., 47:4 (2006), 753–768; Siberian Math. J., 47:4 (2006), 621–633
Citation in format AMSBIB
\Bibitem{GavMak06}
\by A.~L.~Gavrilyuk, A.~A.~Makhnev
\paper Amply regular graphs and block designs
\jour Sibirsk. Mat. Zh.
\yr 2006
\vol 47
\issue 4
\pages 753--768
\mathnet{http://mi.mathnet.ru/smj892}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2265279}
\zmath{https://zbmath.org/?q=an:1150.05393}
\transl
\jour Siberian Math. J.
\yr 2006
\vol 47
\issue 4
\pages 621--633
\crossref{https://doi.org/10.1007/s11202-006-0073-y}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000240044100003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746454250}
Linking options:
  • https://www.mathnet.ru/eng/smj892
  • https://www.mathnet.ru/eng/smj/v47/i4/p753
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
    Statistics & downloads:
    Abstract page:468
    Full-text PDF :133
    References:60
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024