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Mat. Zametki, 2018, Volume 103, Issue 5, Pages 657–666 (Mi mz11492)  

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

The Number of Labeled Outerplanar $k$-Cyclic Graphs

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences

Abstract: A $k$-cyclic graph is a graph with cyclomatic number $k$. An explicit formula for the number of labeled connected outerplanar $k$-cyclic graphs with a given number of vertices is obtained. In addition, such graphs with fixed cyclomatic number $k$ and a large number of vertices are asymptotically enumerated. As a consequence, it is found that, for fixed $k$, almost all labeled connected outerplanar $k$-cyclic graphs with a large number of vertices are cacti.

Keywords: enumeration, labeled graph, connected graph, $k$-cyclic graph, outerplanar graph, cactus, asymptotics.

DOI: https://doi.org/10.4213/mzm11492

Full text: PDF file (427 kB)
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English version:
Mathematical Notes, 2018, 103:5, 694–702

Bibliographic databases:

UDC: 519.175.3
Received: 12.12.2016
Revised: 02.02.2017

Citation: V. A. Voblyi, “The Number of Labeled Outerplanar $k$-Cyclic Graphs”, Mat. Zametki, 103:5 (2018), 657–666; Math. Notes, 103:5 (2018), 694–702

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Voblyi, “On the number of labeled outerplanar $k$-cyclic bridgeless graphs”, J. Appl. Industr. Math., 14:1 (2020), 205–211  mathnet  crossref  crossref
    2. 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
    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, “Ob odnom podkhode k perechisleniyu pomechennykh svyaznykh grafov: obzor rezultatov”, Differentsialnye uravneniya i matematicheskoe modelirovanie, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 188, VINITI RAN, M., 2020, 106–118  mathnet  crossref
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