@article{e46bd9d4359044e78c5debc2cd13fc6c,
title = "On Rationality of Generating Function for the Number of Spanning Trees in Circulant Graphs",
abstract = "Let F(x) = n=1s1,s2, ...,sk(n)xn be the generating function for the number τs1,s2, ...,sk(n) of spanning trees in the circulant graph Cn(s1, s2, ..., sk). We show that F(x) is a rational function with integer coefficients satisfying the property F(x) = F(1/x). A similar result is also true for the circulant graphs C2n(s1, s2, ..., sk, n) of odd valency. We illustrate the obtained results by a series of examples.",
keywords = "Chebyshev polynomial, circulant graph, generating function, spanning tree, JACOBIAN GROUP, COMPLEXITY, FORMULAS",
author = "Mednykh, {A. D.} and Mednykh, {I. A.}",
note = "Publisher Copyright: {\textcopyright} 2020 Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = mar,
day = "1",
doi = "10.1142/S1005386720000085",
language = "English",
volume = "27",
pages = "87--94",
journal = "Algebra Colloquium",
issn = "1005-3867",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",
}