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Diskretn. Anal. Issled. Oper., 2009, Volume 16, Number 5, Pages 52–68 (Mi da587)  

This article is cited in 2 scientific papers (total in 2 papers)

On nonexistence of some perfect 2-colorings of Johnson graphs

I. Yu. Mogilnykhab

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: A perfect coloring in $m$ colors of a graph $G$ with matrix $A=\{a_{ij}\}_{i,j=1,…,m}$ is a coloring of vertex set of $G$ in the set of colors $\{1,…,m\}$ such that the number of vertices of color $j$ adjacent to a fixed vertex of color $i$ does not depend on choice of the last vertex and equals $a_{ij}$. In this paper we obtain a low bound on parameter $a_{ij}$, $i\neq j$, of a perfect coloring of a Johnson graph in two colors. Also we show that some perfect colorings of Johnson graph in two colors do not exist. Bibl. 13.

Keywords: perfect coloring, completely regular code, Johnson scheme.

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Bibliographic databases:
UDC: 621.391.15
Received: 15.05.2009

Citation: I. Yu. Mogilnykh, “On nonexistence of some perfect 2-colorings of Johnson graphs”, Diskretn. Anal. Issled. Oper., 16:5 (2009), 52–68

Citation in format AMSBIB
\Bibitem{Mog09}
\by I.~Yu.~Mogilnykh
\paper On nonexistence of some perfect 2-colorings of Johnson graphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2009
\vol 16
\issue 5
\pages 52--68
\mathnet{http://mi.mathnet.ru/da587}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2590755}
\zmath{https://zbmath.org/?q=an:1249.05132}


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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. S. V. Avgustinovich, I. Yu. Mogilnykh, “Perfect 2-colorings of Johnson graphs $J(8,3)$ and $J(8,4)$”, J. Appl. Industr. Math., 5:1 (2011), 19–30  mathnet  crossref  mathscinet  zmath
    2. J. Borges, J. Rifà, V. A. Zinoviev, “On completely regular codes”, Problems Inform. Transmission, 55:1 (2019), 1–45  mathnet  crossref  crossref  isi  elib
  • Дискретный анализ и исследование операций
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