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Diskretn. Anal. Issled. Oper., Ser. 1, 2006, Volume 13, Number 1, Pages 99–108 (Mi da26)  

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

Sufficient conditions for the existence of a graph with a given variety of balls

K. L. Rychkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: It is proved that for each positive integer $d$ and each collection of integers $\overline\tau=(\tau_0,\tau_1,…,\tau_d)$ such that $\tau_0\geqslant\tau_1\geqslant…\geqslant\tau_d=1$ and $\tau_{d-1}\geqslant d^2+1$, there exists a graph of diameter $d$ whose variety vector of the balls is equal to $\overline\tau$; if $d\geqslant 3$ then there is no graph of diameter $d$ whose variety vector of balls $(\tau_0,\tau_1,…,\tau_d)$ satisfies the condition $\tau_0=\tau_1=…=\tau_{d-1}\leqslant2d-1$.

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English version:
Journal of Applied and Industrial Mathematics, 2007, 1:3, 380–385

Bibliographic databases:

UDC: 519.176
Received: 27.10.2005

Citation: K. L. Rychkov, “Sufficient conditions for the existence of a graph with a given variety of balls”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:1 (2006), 99–108; J. Appl. Industr. Math., 1:3 (2007), 380–385

Citation in format AMSBIB
\Bibitem{Ryc06}
\by K.~L.~Rychkov
\paper Sufficient conditions for the existence of a~graph with a~given variety of balls
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2006
\vol 13
\issue 1
\pages 99--108
\mathnet{http://mi.mathnet.ru/da26}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2258906}
\zmath{https://zbmath.org/?q=an:1249.05100}
\transl
\jour J. Appl. Industr. Math.
\yr 2007
\vol 1
\issue 3
\pages 380--385
\crossref{https://doi.org/10.1134/S1990478907030131}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548696872}


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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. J. Appl. Industr. Math., 2:3 (2008), 341–356  mathnet  crossref  mathscinet  zmath
    2. J. Appl. Industr. Math., 3:1 (2009), 107–116  mathnet  crossref  zmath
    3. T. I. Fedoryaeva, “On graphs with given diameter, number of vertices, and local diversity of balls”, J. Appl. Industr. Math., 5:1 (2011), 44–50  mathnet  crossref  mathscinet  zmath
    4. A. A. Evdokimov, T. I. Fedoryaeva, “On the description problem of the diversity vectors of balls”, J. Appl. Industr. Math., 8:2 (2014), 190–195  mathnet  crossref  mathscinet
    5. T. I. Fedoryaeva, “Vychislenie vektora raznoobraziya sharov zadannogo grafa”, Sib. elektron. matem. izv., 13 (2016), 122–129  mathnet  crossref
    6. T. I. Fedoryaeva, “Stroenie vektora raznoobraziya sharov tipichnogo grafa zadannogo diametra”, Sib. elektron. matem. izv., 13 (2016), 375–387  mathnet  crossref
    7. A. A. Evdokimov, T. I. Fedoryaeva, “Tree-like structure graphs with full diversity of balls”, J. Appl. Industr. Math., 12:1 (2018), 19–27  mathnet  crossref  crossref  elib
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