The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps

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The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps. / Mednykh, A. D.; Mednykh, I. A.; Sokolova, G. K.

In: Siberian Advances in Mathematics, Vol. 35, No. 2, 06.08.2025, p. 146-155.

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

BibTeX

@article{3b38686027a245fc91e1e35efefb023e,

title = "The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps",

abstract = "We describe the structure of the characteristic polynomial of the Laplacian matrix for a circulant graph withnon-fixed jumps. We represent the characteristic polynomial in the form of the product ofalgebraic functions involving roots of linear combinations of Chebyshev polynomials of the firstkind. We show that isthe product of the square of a polynomial with integer coefficients and explicitly described linearpolynomials with integer coefficients. We suggest a formula for the number of rooted spanningforests in such a graph.",

keywords = "Circulant graph, Laplacian matrix, characteristic polynomial, rooted spanning forest",

author = "Mednykh, {A. D.} and Mednykh, {I. A.} and Sokolova, {G. K.}",

note = "The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0005). Mednykh, A. D. The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps / A. D. Mednykh, I. A. Mednykh, G. K. Sokolova // Siberian Advances in Mathematics. – 2025. – Vol. 35, No. 2. – P. 146-155. – DOI 10.1134/S1055134425020063.",

year = "2025",

month = aug,

day = "6",

doi = "10.1134/S1055134425020063",

language = "English",

volume = "35",

pages = "146--155",

journal = "Siberian Advances in Mathematics",

issn = "1055-1344",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps

AU - Mednykh, A. D.

AU - Mednykh, I. A.

AU - Sokolova, G. K.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0005). Mednykh, A. D. The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps / A. D. Mednykh, I. A. Mednykh, G. K. Sokolova // Siberian Advances in Mathematics. – 2025. – Vol. 35, No. 2. – P. 146-155. – DOI 10.1134/S1055134425020063.

PY - 2025/8/6

Y1 - 2025/8/6

N2 - We describe the structure of the characteristic polynomial of the Laplacian matrix for a circulant graph withnon-fixed jumps. We represent the characteristic polynomial in the form of the product ofalgebraic functions involving roots of linear combinations of Chebyshev polynomials of the firstkind. We show that isthe product of the square of a polynomial with integer coefficients and explicitly described linearpolynomials with integer coefficients. We suggest a formula for the number of rooted spanningforests in such a graph.

AB - We describe the structure of the characteristic polynomial of the Laplacian matrix for a circulant graph withnon-fixed jumps. We represent the characteristic polynomial in the form of the product ofalgebraic functions involving roots of linear combinations of Chebyshev polynomials of the firstkind. We show that isthe product of the square of a polynomial with integer coefficients and explicitly described linearpolynomials with integer coefficients. We suggest a formula for the number of rooted spanningforests in such a graph.

KW - Circulant graph

KW - Laplacian matrix

KW - characteristic polynomial

KW - rooted spanning forest

UR - https://www.mendeley.com/catalogue/2a1e6dc1-e0f4-3b79-b430-79286808b852/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105012723246&origin=inward

UR - https://elibrary.ru/item.asp?id=82714811

U2 - 10.1134/S1055134425020063

DO - 10.1134/S1055134425020063

M3 - Article

VL - 35

SP - 146

EP - 155

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 2

ER -

ID: 68771979