@article{523dd0dd773a4a35abbef385e59ddef5,
title = "Counting rooted spanning foresrs in cobordism of two circulant graphs",
abstract = "We consider a family of graphs H-n(s(1), ..., s(k); t(1), ...,t(l)), 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), ..., s(k), t(1), ..., t(l) and the parity of n.",
keywords = "circulant graph, I-graph, Petersen graph, prism graph, spanning forest, Chebyshev polynomial, Mahler measure, TREE FORMULAS, I-GRAPHS, NUMBER, ENUMERATION, COMPLEXITY",
author = "Abrosimov, {N. V.} and Baigonakova, {G. A.} and Grunwald, {L. A.} and Mednykh, {I. A.}",
note = "Funding Information: Abrosimov, N.V., Baigonakova, G.A., Grunwald, L.A., Mednykh, I.A., Counting rooted spanning foresrs in cobordism of two circulant graphs. ⃝c 2020 Abrosimov N.V., Baigonakova G.A., Grunwald L.A., Mednykh I.A. Parts 1–4 of the work were supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation, part 5 was supported by Russian Foundation for Basic Research (project 18-01-00420). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2020",
doi = "10.33048/semi.2020.17.059",
language = "English",
volume = "17",
pages = "814--823",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
}