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Diskretnyi Analiz i Issledovanie Operatsii, 2010, Volume 17, Issue 2, Pages 3–19 (Mi da602)  
This article is cited in 27 scientific papers (total in 27 papers)

Perfect 2-colorings of Johnson graphs $J(8,3)$ and $J(8,4)$

S. V. Avgustinovichab, I. Yu. Mogilnykhab

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (290 kB) Citations (27)
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Abstract: In this paper we list all the matrices of parameters of perfect 2-colorings of Johnson graphs $J(8,3)$ and $J(8,4)$, give some constructions of perfect 2-colorings of Johnson graphs $J(2w,w)$ and $J(2m,3)$. The notion of perfect coloring is a generalization of the notion of completely regular code, introduced by Delsarte. The problem of existence of such structures in Johnson scheme is closely related to the problem of existence of completely regular codes in Johnson graphs, particularly to the Delsarte conjecture on nonexistence of nontrivial constant weight perfect codes, problem of existence of designs and other well-known mathematical problems. Bibl. 19.
Keywords: perfect coloring, Johnson scheme, design.
Received: 10.08.2009
English version:
Journal of Applied and Industrial Mathematics, 2011, Volume 5, Issue 1, Pages 19–30
DOI: https://doi.org/10.1134/S1990478911010030
Bibliographic databases:
Document Type: Article
UDC: 621.391.15
Language: Russian
Citation: S. V. Avgustinovich, I. Yu. Mogilnykh, “Perfect 2-colorings of Johnson graphs $J(8,3)$ and $J(8,4)$”, Diskretn. Anal. Issled. Oper., 17:2 (2010), 3–19; J. Appl. Industr. Math., 5:1 (2011), 19–30
Citation in format AMSBIB
\Bibitem{AvgMog10}
\by S.~V.~Avgustinovich, I.~Yu.~Mogilnykh
\paper Perfect 2-colorings of Johnson graphs $J(8,3)$ and $J(8,4)$
\jour Diskretn. Anal. Issled. Oper.
\yr 2010
\vol 17
\issue 2
\pages 3--19
\mathnet{http://mi.mathnet.ru/da602}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2682086}
\zmath{https://zbmath.org/?q=an:1249.05242}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 1
\pages 19--30
\crossref{https://doi.org/10.1134/S1990478911010030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952318672}
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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