TY - JOUR

T1 - On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials

AU - Mednykh, Ilya A.

N1 - Publisher Copyright: © 2018 Society of Mathematicians, Physicists and Astronomers of Slovenia. 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 -