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Diskretn. Anal. Issled. Oper., 2010, Volume 17, Number 1, Pages 65–74 (Mi da600)  

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

On graphs with given diameter, number of vertices, and local diversity of balls

T. I. Fedoryaeva

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: The $n$-vertex graphs with diameter $d$ and local $t$-diversity of balls, i.e. graphs having $n$ different balls of radius $i$ for every $i\leq t$, in connection with the characterization problem of the diversity vectors of balls of usual connected graphs are studied. For such graphs there exists a lower bound for the number of vertices, defined by the parameters $d$ and $t$. All graphs of the minimal possible order with diameter $d$ and local $t$-diversity of balls (full diversity of balls) are explicitly described up to isomorphism. Moreover, the diversity vector of balls is calculated for any such graph. Ill. 4, bibl. 8.

Keywords: graph, diameter of the graph, metric ball, radius of the ball, number of balls, diversity vector of balls.

Full text: PDF file (263 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2011, 5:1, 44–50

Bibliographic databases:

UDC: 519.17
Received: 16.06.2009
Revised: 08.11.2009

Citation: T. I. Fedoryaeva, “On graphs with given diameter, number of vertices, and local diversity of balls”, Diskretn. Anal. Issled. Oper., 17:1 (2010), 65–74; J. Appl. Industr. Math., 5:1 (2011), 44–50

Citation in format AMSBIB
\Bibitem{Fed10}
\by T.~I.~Fedoryaeva
\paper On graphs with given diameter, number of vertices, and local diversity of balls
\jour Diskretn. Anal. Issled. Oper.
\yr 2010
\vol 17
\issue 1
\pages 65--74
\mathnet{http://mi.mathnet.ru/da600}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2667014}
\zmath{https://zbmath.org/?q=an:1249.05326}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 1
\pages 44--50
\crossref{https://doi.org/10.1134/S1990478911010054}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952318671}


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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. T. I. Fedoryaeva, “Majorants and minorants in the graph class with given number of vertices and diameter”, J. Appl. Industr. Math., 7:2 (2013), 153–165  mathnet  crossref  mathscinet
    2. 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
    3. T. I. Fedoryaeva, “O raznoobrazii sharov grafa zadannogo diametra”, PDM. Prilozhenie, 2015, no. 8, 127–128  mathnet  crossref
    4. T. I. Fedoryaeva, “Vektor raznoobraziya sharov tipichnogo grafa malogo diametra”, Diskretn. analiz i issled. oper., 22:6 (2015), 43–54  mathnet  crossref  mathscinet  elib
    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
  • Дискретный анализ и исследование операций
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