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Matematicheskie Zametki, 2018, Volume 103, Issue 5, Pages 657–666
DOI: https://doi.org/10.4213/mzm11492 (Mi mzm11492) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (427 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm11492
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.
Received: 12.12.2016
Revised: 02.02.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 5, Pages 694–702
DOI: https://doi.org/10.1134/S0001434618050024
Bibliographic databases:
Document Type: Article
UDC: 519.175.3
Language: Russian
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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