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Volume 29, No 4, 2022, P. 5-14

UDC 519.175.3
V. A. Voblyi
On asymptotic enumeration of labeled series-parallel $k$-cyclic graphs

Abstract:
We deduce an asymptotic formula for the number of labeled connected series-parallel $k$-cyclic graphs with given order and fixed number $k$. Under uniform probability distribution, we find the probability that a random labeled connected $n$-vertex $k$-cyclic graph with a fixed $k$ and $n \to \infty$ is a series-parallel graph. In addition, we determine the probability that, under uniform probability distribution, a random labeled connected series-parallel $n$-vertex $k$-cyclic graph with a fixed $k$ and $n \to \infty$ is a cactus.
Bibliogr. 16.

Keywords: enumeration, labeled graph, block, series-parallel graph, $k$-cyclic graph, asymptotics, random graph.

DOI: 10.33048/daio.2022.29.732

Vitaly A. Voblyi1
1. All-Russian Institute for Scientific and Technical Information,
20 Usievich Street, 125190 Moscow, Russia
e-mail: vitvobl@yandex.ru

Received February 7, 2022
Revised April 17, 2022
Accepted April 19, 2022

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