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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 94–112 (Mi znsl5752)  
This article is cited in 5 scientific papers (total in 5 papers)

The sandpile groups of chain-cyclic graphs

I. A. Krepkiy

St. Petersburg State University, Universitetsky pr. 28, Peterhof, 198504 St. Petersburg, Russia
Full-text PDF (246 kB) Citations (5)
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Abstract: Firstly, we consider the graphs obtained by gluing a family of arbitrary finite graphs to the edges of a cyclic graph and prove that the sandpile group of the resulting graph does not depend on a specific way of doing that. Then, we define the class of chain-cyclic graphs, which are the graphs obtained by connecting a finite family of cyclic graphs along a line. Two kinds of formulas for calculating the sandpile groups of chain-cyclic graphs are proved.
Key words and phrases: sandpile group, Smith normal form, chain-cyclic graph.
Received: 26.12.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 200, Issue 6, Pages 698–709
DOI: https://doi.org/10.1007/s10958-014-1961-5
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: English
Citation: I. A. Krepkiy, “The sandpile groups of chain-cyclic graphs”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 94–112; J. Math. Sci. (N. Y.), 200:6 (2014), 698–709
Citation in format AMSBIB
\Bibitem{Kre14}
\by I.~A.~Krepkiy
\paper The sandpile groups of chain-cyclic graphs
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 421
\pages 94--112
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5752}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 200
\issue 6
\pages 698--709
\crossref{https://doi.org/10.1007/s10958-014-1961-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84933068465}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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