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Diskretn. Anal. Issled. Oper., 2015, Volume 22, Number 6, Pages 43–54 (Mi da832)  

This article is cited in 3 scientific papers (total in 3 papers)

The diversity vector of balls of a typical graph of small diameter

T. I. Fedoryaevaab

a Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
b Sobolev Institute of Mathematics, 4 Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: For ordinary connected graphs, the diversity vectors of balls ($i$th component of the vector is equal to the number of different balls of radius $i$) are studied asymptotically. The asymptotic behavior of the number of graphs of small diameter with full diversity of balls is investigated. The diversity vector of balls of a typical graph of the given small diameter is calculated. Asymptotically exact value of the number of labeled $n$-vertex graphs of diameter 3 is obtained. Ill. 2, bibliogr. 12.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00507


DOI: https://doi.org/10.17377/daio.2015.22.512

Full text: PDF file (278 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 519.1+519.173
Received: 20.09.2015
Revised: 26.10.2015

Citation: T. I. Fedoryaeva, “The diversity vector of balls of a typical graph of small diameter”, Diskretn. Anal. Issled. Oper., 22:6 (2015), 43–54

Citation in format AMSBIB
\Bibitem{Fed15}
\by T.~I.~Fedoryaeva
\paper The diversity vector of balls of a~typical graph of small diameter
\jour Diskretn. Anal. Issled. Oper.
\yr 2015
\vol 22
\issue 6
\pages 43--54
\mathnet{http://mi.mathnet.ru/da832}
\crossref{https://doi.org/10.17377/daio.2015.22.512}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3497822}
\elib{http://elibrary.ru/item.asp?id=25124389}


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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, “Vychislenie vektora raznoobraziya sharov zadannogo grafa”, Sib. elektron. matem. izv., 13 (2016), 122–129  mathnet  crossref
    2. T. I. Fedoryaeva, “Stroenie vektora raznoobraziya sharov tipichnogo grafa zadannogo diametra”, Sib. elektron. matem. izv., 13 (2016), 375–387  mathnet  crossref
    3. T. I. Fedoryaeva, “Asymptotic approximation for the number of graphs”, J. Appl. Industr. Math., 11:2 (2017), 204–214  mathnet  crossref  crossref  elib
  • Дискретный анализ и исследование операций
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