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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 122–129 (Mi semr660)  

This article is cited in 1 scientific paper (total in 1 paper)

Discrete mathematics and mathematical cybernetics

Computing the diversity vectors of balls of a given graph

T. I. Fedoryaeva

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: For an ordinary finite not necessarily connected graph, the diversity vector of balls ($i$th component of the vector is equal to the number of different balls of radius i) is studied. Properties of metric balls in such graphs are established. In particular, a coincidence condition of balls with centers at different vertices is found. Based on these properties, the algorithm of computing the diversity vector of balls of a given graph $G=(V,E)$ with a running time $O(|V|^3)$ is developed.

Keywords: graph, distance, distance matrix, metric ball, number of balls, diversity vector of balls, algorithm, complexity.

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


DOI: https://doi.org/10.17377/semi.2016.13.010

Full text: PDF file (153 kB)
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Bibliographic databases:

UDC: 519.173+519.178
MSC: 05C12+05C85
Received February 18, 2016, published March 3, 2016

Citation: T. I. Fedoryaeva, “Computing the diversity vectors of balls of a given graph”, Sib. Èlektron. Mat. Izv., 13 (2016), 122–129

Citation in format AMSBIB
\Bibitem{Fed16}
\by T.~I.~Fedoryaeva
\paper Computing the diversity vectors of balls of a given graph
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 122--129
\mathnet{http://mi.mathnet.ru/semr660}
\crossref{https://doi.org/10.17377/semi.2016.13.010}


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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, “Stroenie vektora raznoobraziya sharov tipichnogo grafa zadannogo diametra”, Sib. elektron. matem. izv., 13 (2016), 375–387  mathnet  crossref
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