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Prikl. Diskr. Mat., 2020, Number 47, Pages 57–61 (Mi pdm694)  

This article is cited in 4 scientific papers (total in 4 papers)

Applied Graph Theory

The number of labeled tetracyclic series-parallel blocks

V. A. Voblyi

All-Russian Institut for Scientific and Technical Information, Moscow, Russia

Abstract: A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. Such graphs are used in the construction of reliable communication networks. Let $TB(n)$ be the number of labeled series-parallel tetracyclic blocks with $n$ vertices. The formula $TB(n)=\dfrac{n!}{80640}(n^5+30n^4+257n^3+768n^2+960n+504)\dbinom{n-3}{3}$ is obtained. It is proved that with a uniform probability distribution, the probability that the labeled tetracyclic block is a series-parallel graph is asymptotically $3/11$.

Keywords: labeled graph, tetracyclic graph, series-parallel graph, block, enumeration, asymptotics.

DOI: https://doi.org/10.17223/20710410/47/5

Full text: PDF file (638 kB)
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Bibliographic databases:

UDC: 519.175.3

Citation: V. A. Voblyi, “The number of labeled tetracyclic series-parallel blocks”, Prikl. Diskr. Mat., 2020, no. 47, 57–61

Citation in format AMSBIB
\Bibitem{Vob20}
\by V.~A.~Voblyi
\paper The number of labeled tetracyclic series-parallel~blocks
\jour Prikl. Diskr. Mat.
\yr 2020
\issue 47
\pages 57--61
\mathnet{http://mi.mathnet.ru/pdm694}
\crossref{https://doi.org/10.17223/20710410/47/5}


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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. V. A. Voblyi, “Perechislenie pomechennykh posledovatelno-parallelnykh tritsiklicheskikh grafov”, Algebra, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 177, VINITI RAN, M., 2020, 132–136  mathnet  crossref
    2. V. A. Voblyi, “Novaya formula dlya chisla pomechennykh posledovatelno-parallelnykh 2-svyaznykh grafov”, Trudy mezhdunarodnoi konferentsii Klassicheskaya i sovremennaya geometriya, posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva. Moskva, 2225 aprelya 2019 g. Chast 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 182, VINITI RAN, M., 2020, 10–13  mathnet  crossref
    3. V. A. Voblyi, “Asimptoticheskoe perechislenie pomechennykh posledovatelno-parallelnykh tetratsiklicheskikh grafov”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 31–35  mathnet  crossref
    4. V. A. Voblyi, “On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs”, J. Appl. Industr. Math., 15:1 (2021), 169–174  mathnet  crossref  crossref
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