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This article is cited in 2 scientific papers (total in 2 papers)
Real, complex and functional analysis
Counting rooted spanning forests in cobordism of two circulant graphs
N. V. Abrosimovab, G. A. Baigonakovac, L. A. Grunwaldab, I. A. Mednykhab a Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
c Gorno-Altaysk State University, 34, Socialisticheskaya str., Gorno-Altaysk, 639000, Russia
Abstract:
We consider a family of graphs $H_n(s_1,\dots,s_k;t_1,\dots,t_\ell),$ which is a generalization of the family of $I$-graphs, which in turn, includes the generalized Petersen graphs and the prism graphs. We present an explicit formula for the number $f_{H}(n)$ of rooted spanning forests in these graphs in terms of Chebyshev polynomials and find its asymptotics. Also, we show that the number of rooted spanning forests can be represented in the form $f_{H}(n)=p a(n)^2,$ where $a(n)$ is an integer sequence and $p$ is a prescribed integer depending on the number of odd elements in the sequence $s_{1},\dots,s_{k},t_{1},\dots,t_{\ell}$ and the parity of $n$.
Keywords:
circulant graph, $I$-graph, Petersen graph, prism graph, spanning forest, Chebyshev polynomial, Mahler measure.
Received January 4, 2020, published June 19, 2020
Citation:
N. V. Abrosimov, G. A. Baigonakova, L. A. Grunwald, I. A. Mednykh, “Counting rooted spanning forests in cobordism of two circulant graphs”, Sib. Èlektron. Mat. Izv., 17 (2020), 814–823
Linking options:
https://www.mathnet.ru/eng/semr1253 https://www.mathnet.ru/eng/semr/v17/p814
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Abstract page: | 172 | Full-text PDF : | 98 | References: | 14 |
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