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Diskretn. Anal. Issled. Oper., 2010, Volume 17, Number 2, Pages 3–19 (Mi da602)  

This article is cited in 7 scientific papers (total in 7 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

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.

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English version:
Journal of Applied and Industrial Mathematics, 2011, 5:1, 19–30

Bibliographic databases:

Document Type: Article
UDC: 621.391.15
Received: 10.08.2009

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{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952318672}


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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. S. V. Avgustinovich, M. A. Lisitsyna, “Perfect 2-colorings of transitive cubic graphs”, J. Appl. Industr. Math., 5:4 (2011), 519–528  mathnet  crossref  mathscinet  zmath
    2. S. V. Avgustinovich, A. Yu. Vasil'eva, I. V. Sergeeva, “Distance regular colorings of the infinite rectangular grid”, J. Appl. Industr. Math., 6:3 (2012), 280–285  mathnet  crossref  mathscinet  zmath
    3. K. V. Vorobev, “On the embedding of eigenfunctions of the Johnson graph into eigenfunctions of the Hamming graph”, J. Appl. Industr. Math., 8:1 (2014), 136–142  mathnet  crossref  mathscinet
    4. Alaeiyan M.H., Karami H., “Perfect 2-Colorings of the Platonic Graphs”, Int. J. Nonlinear Anal. Appl., 8:2 (2017), 29–35  crossref  zmath  isi
    5. Alaeiyan M., Mehrabani A., “Perfect 3-Colorings of the Cubic Graphs of Order 10”, Electron. J. Graph Theory Appl., 5:2 (2017), 194–206  crossref  mathscinet  isi  scopus
    6. Alaeiyan M.H., Abedi A., “Perfect 3-Colorings of the Johnson Graphs J (4,2), J (5,2), J (6,2) and Petersen Graph”, ARS Comb., 140 (2018), 199–213  mathscinet  zmath  isi
    7. Alaeiyan M., Mehrabani A., “Perfect 3-Colorings of Cubic Graphs of Order 8”, Armen. J. Math., 10:2 (2018), 1–11  mathscinet  isi
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