The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps Full article
| Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2025, Volume: 35, Number: 2, Pages: 146–155 Pages count : 10 DOI: 10.1134/S1055134425020063 | ||||
| Tags | Circulant graph, rooted spanning forest, characteristic polynomial, Laplacian matrix | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0005 |
Abstract:
We describe the structure of the characteristic polynomial χL of the Laplacian matrix
for a circulant graph with non-fixed jumps. We represent the characteristic polynomial in the form of
the product of algebraic functions involving roots of linear combinations of Chebyshev polynomials of
the first kind. We show that χL is the product of the square of a polynomial with integer coefficients
and explicitly described linear polynomials with integer coefficients. We suggest a formula for
the number of rooted spanning forests in such a graph.
Cite:
Mednykh A.D.
, Mednykh I.A.
, Sokolova G.K.
The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps
Siberian Advances in Mathematics. 2025. V.35. N2. P.146–155. DOI: 10.1134/S1055134425020063 Scopus РИНЦ
The Structure of the Characteristic Polynomial of the Laplacian Matrix for a Circulant Graph with Non-Fixed Jumps
Siberian Advances in Mathematics. 2025. V.35. N2. P.146–155. DOI: 10.1134/S1055134425020063 Scopus РИНЦ
Original:
Медных А.Д.
, Медных И.А.
, Соколова Г.К.
Структура характеристического полинома матрицы Лапласа циркулянтного графа с нефиксированными скачками
Математические труды. 2025. Т.28. №1. С.94–112. DOI: 10.25205/1560-750X-2025-28-1-94-112 РИНЦ
Структура характеристического полинома матрицы Лапласа циркулянтного графа с нефиксированными скачками
Математические труды. 2025. Т.28. №1. С.94–112. DOI: 10.25205/1560-750X-2025-28-1-94-112 РИНЦ
Dates:
| Submitted: | Sep 18, 2024 |
| Accepted: | Oct 30, 2024 |
| Published print: | Aug 6, 2025 |
| Published online: | Aug 6, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105012723246 |
| Elibrary: | 82714811 |
Citing:
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