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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:2, 296-303

Volume 24, No 2, 2017, P. 18-31

UDC 519.175.3
V. A. Voblyi and A. K. Meleshko
Enumeration of labeled outerplanar bicyclic and tricyclic graphs

Abstract:
The class of outerplanar graphs is used for testing the average complexity of algorithms on graphs. A random labeled outerplanar graph can be generated by a polynomial algorithm based on the results of an enumeration of such graphs. By a bicyclic (tricyclic) graph we mean a connected graph with cyclomatic number 2 (respectively, 3). We find explicit formulas for the number of labeled connected outerplanar bicyclic and tricyclic graphs with $n$ vertices and also obtain asymptotics for the number of these graphs for large $n$. Moreover, we obtain explicit formulas for the number of labeled outerplanar bicyclic and tricyclic $n$-vertex blocks and deduce the corresponding asymptotics for large $n$.
Tab. 1, illustr. 4, bibliogr. 15.

Keywords: enumeration, labeled graph, outerplanar graph, bicyclic graph, tricyclic graph, asymptotics.

DOI: 10.17377/daio.2017.24.544

Vitaly A. Voblyi 1
Anna K. Meleshko 1

1. Bauman Moscow State University,
5 Bld. 1 Vtoraya Baumanskaya St., 105005 Moscow, Russia
e-mail: vitvobl@yandex.ru, bakmeleshko@gmail.com

Revised 11 October 2016

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