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On the Structure of Laplacian Characteristic Polynomial of Circulant Graphs Full article

Journal Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362
Output data Year: 2024, Volume: 109, Number: 1, Pages: 25–29 Pages count : 5 DOI: 10.1134/s1064562424701771
Tags circulant graph, Laplacian matrix, eigenvalues, rooted spanning tree
Authors Kwon Young Soo 1 , Mednykh Alexander 2,3 , Медных И.А. 2,3
Affiliations
1 Yeungnam University, Gyeongsan, Republic of Korea
2 Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
3 Novosibirsk State University, Novosibirsk, Russia

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0005

Abstract: The present work deals with the characteristic polynomial of Laplacian matrix for circulant graphs. We show that it can be decomposed into a finite product of algebraic function evaluated at the roots of a linear combination of Chebyshev polynomials. As an important consequence of this result, we get the periodicity of characteristic polynomials evaluated at the prescribed integer values. Moreover, we can show that the characteristic polynomials of circulant graphs are always perfect squares up to explicitly given linear factors.
Cite: Kwon Y.S. , Mednykh A. , Медных И.А.
On the Structure of Laplacian Characteristic Polynomial of Circulant Graphs
Doklady Mathematics. 2024. V.109. N1. P.25–29. DOI: 10.1134/s1064562424701771 WOS Scopus РИНЦ OpenAlex
Original: Квон Й.С. , Медных А.Д. , Медных И.А.
О структуре характеристического полинома Лапласа для циркулянтных графов
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2024. Т.515. №1. С.34-39. DOI: 10.31857/S2686954324010059 РИНЦ OpenAlex
Dates:
Submitted: Apr 21, 2023
Accepted: Jan 24, 2024
Published print: Mar 11, 2024
Published online: Mar 11, 2024
Identifiers:
Web of science: WOS:001180328000005
Scopus: 2-s2.0-85187184179
Elibrary: 66924487
OpenAlex: W4392646553
Citing: Пока нет цитирований
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