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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 122–129
DOI: https://doi.org/10.17377/semi.2016.13.010
(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
Full-text PDF (153 kB) Citations (1)
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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
Received February 18, 2016, published March 3, 2016
Bibliographic databases:
Document Type: Article
UDC: 519.173+519.178
MSC: 05C12+05C85
Language: Russian
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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  • https://www.mathnet.ru/eng/semr/v13/p122
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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