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Diskretn. Anal. Issled. Oper., 2017, Volume 24, Number 2, Pages 18–31 (Mi da867)  

Enumeration of labeled outerplanar bicyclic and tricyclic graphs

V. A. Voblyi, A. K. Meleshko

Bauman Moscow State University, 5 Bld. 1 Vtoraya Baumanskaya St., 105005 Moscow, Russia

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: https://doi.org/10.17377/daio.2017.24.544

Full text: PDF file (320 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:2, 296–303

UDC: 519.175.3
Received: 10.05.2016
Revised: 11.10.2016

Citation: V. A. Voblyi, A. K. Meleshko, “Enumeration of labeled outerplanar bicyclic and tricyclic graphs”, Diskretn. Anal. Issled. Oper., 24:2 (2017), 18–31; J. Appl. Industr. Math., 11:2 (2017), 296–303

Citation in format AMSBIB
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\by V.~A.~Voblyi, A.~K.~Meleshko
\paper Enumeration of labeled outerplanar bicyclic and tricyclic graphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2017
\vol 24
\issue 2
\pages 18--31
\mathnet{http://mi.mathnet.ru/da867}
\crossref{https://doi.org/10.17377/daio.2017.24.544}
\elib{http://elibrary.ru/item.asp?id=29275512}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 2
\pages 296--303
\crossref{https://doi.org/10.1134/S1990478917020168}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019662440}


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