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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Issue 2, Pages 5–20 (Mi da842)  

This article is cited in 9 scientific papers (total in 9 papers)

Enumeration of labeled connected graphs with given order and number of edges

V. A. Voblyi

Bauman Moscow State University, 5 2nd Baumanskaya St., 105005, Moscow, Russia

Abstract: We deduce a new formula for the number of labeled connected graphs with a given order and number of edges in terms of the block generating function. Applying this formula, we exactly and asymptotically enumerate cacti with given order and cyclomatic number. Tab. 1, bibliogr. 22.

Keywords: enumeration, labeled graph, block, cactus, asymptotics.

DOI: https://doi.org/10.17377/daio.2016.23.501

Full text: PDF file (289 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2016, 10:2, 302–310

Bibliographic databases:

UDC: 519.175.3
Received: 13.07.2015
Revised: 14.12.2015

Citation: V. A. Voblyi, “Enumeration of labeled connected graphs with given order and number of edges”, Diskretn. Anal. Issled. Oper., 23:2 (2016), 5–20; J. Appl. Industr. Math., 10:2 (2016), 302–310

Citation in format AMSBIB
\Bibitem{Vob16}
\by V.~A.~Voblyi
\paper Enumeration of labeled connected graphs with given order and number of edges
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 2
\pages 5--20
\mathnet{http://mi.mathnet.ru/da842}
\crossref{https://doi.org/10.17377/daio.2016.23.501}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3557591}
\elib{https://elibrary.ru/item.asp?id=26129764}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 2
\pages 302--310
\crossref{https://doi.org/10.1134/S1990478916020149}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971219376}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Voblyi, “Enumeration of Labeled Geodetic Graphs with Small Cyclomatic Number”, Math. Notes, 101:5 (2017), 790–794  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. A. Voblyi, “The Number of Labeled Outerplanar $k$-Cyclic Graphs”, Math. Notes, 103:5 (2018), 694–702  mathnet  crossref  crossref  mathscinet  isi  elib
    3. V. A. Voblyi, “The second Riddel relation and its consequences”, J. Appl. Industr. Math., 13:1 (2019), 168–174  mathnet  crossref  crossref
    4. V. A. Voblyi, “On the Asymptotic Enumeration of Labeled Connected $k$-Cyclic Graphs without Bridges”, Math. Notes, 107:2 (2020), 350–352  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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
    6. 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
    7. 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
    8. 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
    9. V. A. Voblyi, “Perechislenie pomechennykh eilerovykh pentatsiklicheskikh grafov”, PDM, 2020, no. 50, 87–92  mathnet  crossref
  • Дискретный анализ и исследование операций
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