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Prikladnaya Diskretnaya Matematika, 2011, Number 4(14), Pages 42–55 (Mi pdm350)  

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

Applied Graph Theory

Multiplicities of sums in the explicit formulae for counting fixed length cycles in undirected graphs

A. N. Voropaev

Petrozavodsk State University, Petrozavodsk, Russia
Full-text PDF (683 kB) Citations (1)
References:
Abstract: An explicit formula for counting $k$-cycles in graphs is the combination of sums corresponding to the shapes of closed $k$-walks. It was shown that the maximum multiplicity of a sum in the formula is $[k/2]$ for, starting with $k=8$. In this work, we study the maximum sum multiplicity for some families of graphs: bipartite, triangle-free, planar, maximum vertex degree three, and their intersections. When $k$ is large, the biparticity and degree boundednesses are the only properties which decrease the maximum sum multiplicity by 1, providing $k\equiv2,3\pmod4$. Some combinations of properties in the case of $k\leq20$ yield the decrease by 1 or 2.
Keywords: counting cycles in graphs, shapes of closed walks, prism graphs.
Document Type: Article
UDC: 519.177+519.174.2+519.171.4
Language: Russian
Citation: A. N. Voropaev, “Multiplicities of sums in the explicit formulae for counting fixed length cycles in undirected graphs”, Prikl. Diskr. Mat., 2011, no. 4(14), 42–55
Citation in format AMSBIB
\Bibitem{Vor11}
\by A.~N.~Voropaev
\paper Multiplicities of sums in the explicit formulae for counting fixed length cycles in undirected graphs
\jour Prikl. Diskr. Mat.
\yr 2011
\issue 4(14)
\pages 42--55
\mathnet{http://mi.mathnet.ru/pdm350}
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  • https://www.mathnet.ru/eng/pdm/y2011/i4/p42
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Прикладная дискретная математика
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    References:49
     
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