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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 94–112
(Mi znsl5752)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl5752 https://www.mathnet.ru/eng/znsl/v421/p94
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Abstract page: | 160 | Full-text PDF : | 44 | References: | 27 |
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