Complexity of the circulant foliation over a graph

Standard

Complexity of the circulant foliation over a graph. / Kwon, Y. S.; Mednykh, A. D.; Mednykh, I. A.

In: Journal of Algebraic Combinatorics, Vol. 53, No. 1, 02.2021, p. 115-129.

Research output: Contribution to journal › Article › peer-review

Harvard

Kwon, YS, Mednykh, AD & Mednykh, IA 2021, 'Complexity of the circulant foliation over a graph', Journal of Algebraic Combinatorics, vol. 53, no. 1, pp. 115-129. https://doi.org/10.1007/s10801-019-00921-7

APA

Kwon, Y. S., Mednykh, A. D., & Mednykh, I. A. (2021). Complexity of the circulant foliation over a graph. Journal of Algebraic Combinatorics, 53(1), 115-129. https://doi.org/10.1007/s10801-019-00921-7

Vancouver

Kwon YS, Mednykh AD , Mednykh IA. Complexity of the circulant foliation over a graph. Journal of Algebraic Combinatorics. 2021 Feb;53(1):115-129. doi: 10.1007/s10801-019-00921-7

Author

Kwon, Y. S. ; Mednykh, A. D. ; Mednykh, I. A. / Complexity of the circulant foliation over a graph. In: Journal of Algebraic Combinatorics. 2021 ; Vol. 53, No. 1. pp. 115-129.

BibTeX

@article{8d0df5517cab40a580ed34edc77f9a91,

title = "Complexity of the circulant foliation over a graph",

abstract = "In the present paper, we investigate the complexity of infinite family of graphs Hn=Hn(G1,G2,…,Gm) obtained as a circulant foliation over a graph H on m vertices with fibers G1,G2,…,Gm. Each fiber Gi=Cn(si,1,si,2,…,si,ki) of this foliation is the circulant graph on n vertices with jumps si,1,si,2,…,si,ki. This family includes the family of generalized Petersen graphs, I-graphs, sandwiches of circulant graphs, discrete torus graphs and others. We obtain a closed formula for the number τ(n) of spanning trees in Hn in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as n→ ∞.",

keywords = "Chebyshev polynomials, Circulant graphs, I-graphs, Laplacian matrices, Petersen graphs, Spanning trees, NUMBER, JACOBIAN GROUP, COUNTING SPANNING-TREES, FORMULAS",

author = "Kwon, {Y. S.} and Mednykh, {A. D.} and Mednykh, {I. A.}",

year = "2021",

month = feb,

doi = "10.1007/s10801-019-00921-7",

language = "English",

volume = "53",

pages = "115--129",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer Netherlands",

number = "1",

}

RIS

TY - JOUR

T1 - Complexity of the circulant foliation over a graph

AU - Kwon, Y. S.

AU - Mednykh, A. D.

AU - Mednykh, I. A.

PY - 2021/2

Y1 - 2021/2

N2 - In the present paper, we investigate the complexity of infinite family of graphs Hn=Hn(G1,G2,…,Gm) obtained as a circulant foliation over a graph H on m vertices with fibers G1,G2,…,Gm. Each fiber Gi=Cn(si,1,si,2,…,si,ki) of this foliation is the circulant graph on n vertices with jumps si,1,si,2,…,si,ki. This family includes the family of generalized Petersen graphs, I-graphs, sandwiches of circulant graphs, discrete torus graphs and others. We obtain a closed formula for the number τ(n) of spanning trees in Hn in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as n→ ∞.

AB - In the present paper, we investigate the complexity of infinite family of graphs Hn=Hn(G1,G2,…,Gm) obtained as a circulant foliation over a graph H on m vertices with fibers G1,G2,…,Gm. Each fiber Gi=Cn(si,1,si,2,…,si,ki) of this foliation is the circulant graph on n vertices with jumps si,1,si,2,…,si,ki. This family includes the family of generalized Petersen graphs, I-graphs, sandwiches of circulant graphs, discrete torus graphs and others. We obtain a closed formula for the number τ(n) of spanning trees in Hn in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as n→ ∞.

KW - Chebyshev polynomials

KW - Circulant graphs

KW - I-graphs

KW - Laplacian matrices

KW - Petersen graphs

KW - Spanning trees

KW - NUMBER

KW - JACOBIAN GROUP

KW - COUNTING SPANNING-TREES

KW - FORMULAS

UR - http://www.scopus.com/inward/record.url?scp=85079637930&partnerID=8YFLogxK

U2 - 10.1007/s10801-019-00921-7

DO - 10.1007/s10801-019-00921-7

M3 - Article

AN - SCOPUS:85079637930

VL - 53

SP - 115

EP - 129

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

IS - 1

ER -

ID: 23594903