TY - JOUR
T1 - On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials
AU - Mednykh, Ilya A.
N1 - Funding Information:
The results of this work were partially supported by the Russian Foundation for Basic Research (grants 16-31-00138, 18-01-00420 and 18-501-51021) and by the program of fundamental researches of the SB RAS no.I.1.2., project 0314-2016-0007 and the Slovenian-Russian grant (2016-2017).
Publisher Copyright:
© 2018 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2018
Y1 - 2018
N2 - We consider a family of I-graphs I(n,k,l), which is a generalization of the class of generalized Petersen graphs. In the present paper, we provide a new method for counting Jacobian group of the I-graph I(n,k,l). We show that the minimum number of generators of Jac(I(n,k,l)) is at least two and at most 2k+2l−1. Also, we obtain a closed formula for the number of spanning trees of I(n,k,l) in terms of Chebyshev polynomials. We investigate some arithmetical properties of this number and its asymptotic behaviour.
AB - We consider a family of I-graphs I(n,k,l), which is a generalization of the class of generalized Petersen graphs. In the present paper, we provide a new method for counting Jacobian group of the I-graph I(n,k,l). We show that the minimum number of generators of Jac(I(n,k,l)) is at least two and at most 2k+2l−1. Also, we obtain a closed formula for the number of spanning trees of I(n,k,l) in terms of Chebyshev polynomials. We investigate some arithmetical properties of this number and its asymptotic behaviour.
KW - Chebyshev polynomial
KW - I-graph
KW - Jacobian group
KW - Petersen graph
KW - Spanning tree
UR - http://www.scopus.com/inward/record.url?scp=85062831812&partnerID=8YFLogxK
U2 - 10.26493/1855-3974.1355.576
DO - 10.26493/1855-3974.1355.576
M3 - Article
AN - SCOPUS:85062831812
VL - 15
SP - 467
EP - 485
JO - Ars Mathematica Contemporanea
JF - Ars Mathematica Contemporanea
SN - 1855-3966
IS - 2
ER -