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Diskretnyi Analiz i Issledovanie Operatsii, 2021, Volume 28, Issue 1, Pages 5–14
DOI: https://doi.org/10.33048/daio.2021.28.693 (Mi da1271) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information of RAS 20 Usievich Street, 125190 Moscow, Russia
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DOI: https://doi.org/10.33048/daio.2021.28.693
Abstract: We deduce an explicit formula for the number of labeled series-parallel $k$-cyclic $n$-vertex $2$-connected graphs and find the corresponding asymptotics for a large number of vertices and a fixed $k$. Under the uniform probability distribution, an asymptotic formula is obtained for the probability that a random $n$-vertex $k$-cyclic $2$-connected graph with a large number of vertices and a fixed $k$ is a series-parallel graph. Tab. 1, bibliogr. 11.
Keywords: enumeration, labeled graph, series-parallel graph, $k$-cyclic graph, asymptotics, random graph.
Received: 11.06.2020
Revised: 20.10.2020
Accepted: 22.10.2020
English version:
Journal of Applied and Industrial Mathematics, 2021, Volume 15, Issue 1, Pages 169–174
DOI: https://doi.org/10.1134/S1990478921010154
Bibliographic databases:
Document Type: Article
UDC: 519.175.3
Language: Russian
Citation: V. A. Voblyi, “On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs”, Diskretn. Anal. Issled. Oper., 28:1 (2021), 5–14; J. Appl. Industr. Math., 15:1 (2021), 169–174
Citation in format AMSBIB
\Bibitem{Vob21}
\by V.~A.~Voblyi
\paper On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2021
\vol 28
\issue 1
\pages 5--14
\mathnet{http://mi.mathnet.ru/da1271}
\crossref{https://doi.org/10.33048/daio.2021.28.693}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 1
\pages 169--174
\crossref{https://doi.org/10.1134/S1990478921010154}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85104701225}
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    • This publication is cited in the following 1 articles:
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