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Diskretn. Anal. Issled. Oper., 2019, Volume 26, Issue 1, Pages 20–32 (Mi da915)  

This article is cited in 10 scientific papers (total in 10 papers)

The second Riddel relation and its consequences

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information RAS, 20 Usievicha St., 125190 Moscow, Russia

Abstract: The second Riddell relation relates the generating functions for the number of labeled connected graphs and the number of labeled blocks. We consider the conditions under which this relation is true for a subclass of connected graphs. Under these conditions, the formulas are valid that express the number of graphs from a subclass of labeled connected graphs trough the generating function of their blocks. By way of application, we obtain expressions for the numbers of labeled connected and 2-connected series-parallel graphs. Bibliogr. 22.

Keywords: enumeration, labeled graph, connected graph, 2-connected graph, generating function, block-stable class, series-parallel graph.

DOI: https://doi.org/10.33048/daio.2019.26.615

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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:1, 168–174

UDC: 519.175.3
Received: 03.04.2018
Revised: 01.10.2018

Citation: V. A. Voblyi, “The second Riddel relation and its consequences”, Diskretn. Anal. Issled. Oper., 26:1 (2019), 20–32; J. Appl. Industr. Math., 13:1 (2019), 168–174

Citation in format AMSBIB
\by V.~A.~Voblyi
\paper The second Riddel relation and its consequences
\jour Diskretn. Anal. Issled. Oper.
\yr 2019
\vol 26
\issue 1
\pages 20--32
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 1
\pages 168--174

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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, “Chislo pomechennykh tetratsiklicheskikh posledovatelno-parallelnykh blokov”, PDM, 2020, no. 47, 57–61  mathnet  crossref
    3. 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
    4. V. A. Voblyi, “An Explicit Formula for the Number of Labeled Series-Parallel $k$-Cyclic Blocks”, Math. Notes, 108:4 (2020), 608–610  mathnet  crossref  crossref  isi  elib
    5. V. A. Voblyi, “Novaya formula dlya chisla pomechennykh posledovatelno-parallelnykh 2-svyaznykh grafov”, Trudy mezhdunarodnoi konferentsii Klassicheskaya i sovremennaya geometriya, posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva. Moskva, 2225 aprelya 2019 g. Chast 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 182, VINITI RAN, M., 2020, 10–13  mathnet  crossref
    6. 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
    7. V. A. Voblyi, “Ob odnom podkhode k perechisleniyu pomechennykh svyaznykh grafov: obzor rezultatov”, Differentsialnye uravneniyai matematicheskoe modelirovanie, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 188, VINITI RAN, M., 2020, 106–118  mathnet  crossref
    8. V. A. Voblyi, “Perechislenie pomechennykh eilerovykh pentatsiklicheskikh grafov”, PDM, 2020, no. 50, 87–92  mathnet  crossref
    9. V. A. Voblyi, “Refinement of the Asymptotics of the Number of Labeled Series-Parallel Graphs”, Math. Notes, 109:6 (2021), 986–989  mathnet  crossref  crossref  isi
    10. V. A. Voblyi, “On the enumeration of labeled series-parallel $k$-cyclic $2$-connected graphs”, J. Appl. Industr. Math., 15:1 (2021), 169–174  mathnet  crossref  crossref
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