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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 1, Pages 58–76 (Mi da719)  

This article is cited in 6 scientific papers (total in 6 papers)

Majorants and minorants in the graph class with given number of vertices and diameter

T. I. Fedoryaeva

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

Abstract: Majorants (minorants), i.e., extremal graphs such that for any $i\ge0$ exact upper (lower) estimates for the number of different balls of the radius $i$ are attained at, are studied in the class of the $n$-vertex graphs with diameter $d$. For all parameters $n$ and $d$, the minorants are described explicitly. It is found out when the majorants exist in the class of $n$-vertex graphs with diameter $d$, and the corresponding extremal graphs are described. Il. 9, bibliogr. 8.

Keywords: graph, metric ball, radius of the ball, the number of balls, estimate of the number of balls, extremal graph.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:2, 153–165

Bibliographic databases:

UDC: 519.1+519.173+519.176
Received: 23.03.2012
Revised: 17.05.2012

Citation: T. I. Fedoryaeva, “Majorants and minorants in the graph class with given number of vertices and diameter”, Diskretn. Anal. Issled. Oper., 20:1 (2013), 58–76; J. Appl. Industr. Math., 7:2 (2013), 153–165

Citation in format AMSBIB
\Bibitem{Fed13}
\by T.~I.~Fedoryaeva
\paper Majorants and minorants in the graph class with given number of vertices and diameter
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 1
\pages 58--76
\mathnet{http://mi.mathnet.ru/da719}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3088149}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 2
\pages 153--165
\crossref{https://doi.org/10.1134/S199047891302004X}


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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. 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
    2. T. I. Fedoryaeva, “O raznoobrazii sharov grafa zadannogo diametra”, PDM. Prilozhenie, 2015, no. 8, 127–128  mathnet  crossref
    3. T. I. Fedoryaeva, “Vektor raznoobraziya sharov tipichnogo grafa malogo diametra”, Diskretn. analiz i issled. oper., 22:6 (2015), 43–54  mathnet  crossref  mathscinet  elib
    4. T. I. Fedoryaeva, “Vychislenie vektora raznoobraziya sharov zadannogo grafa”, Sib. elektron. matem. izv., 13 (2016), 122–129  mathnet  crossref
    5. T. I. Fedoryaeva, “Stroenie vektora raznoobraziya sharov tipichnogo grafa zadannogo diametra”, Sib. elektron. matem. izv., 13 (2016), 375–387  mathnet  crossref
    6. 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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