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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Вещественный, комплексный и и функциональный анализ
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
Аннотация:
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 $n$.
Ключевые слова:
circulant graph, $I$-graph, Petersen graph, prism graph, spanning forest, Chebyshev polynomial, Mahler measure.
Поступила 4 января 2020 г., опубликована 19 июня 2020 г.
Образец цитирования:
N. V. Abrosimov, G. A. Baigonakova, L. A. Grunwald, I. A. Mednykh, “Counting rooted spanning forests in cobordism of two circulant graphs”, Сиб. электрон. матем. изв., 17 (2020), 814–823
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1253 https://www.mathnet.ru/rus/semr/v17/p814
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