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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 515, Pages 34–39
DOI: https://doi.org/10.31857/S2686954324010059 (Mi danma489) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On the structure of Laplacian characteristic polynomial of circulant graphs

Y. S. Kwona, A. D. Mednykhbc, I. A. Mednykhbc

a Yeungnam University, Gyeongsan, Republic of Korea
b Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
c Novosibirsk State University, Novosibirsk, Russian Federation
Full-text PDF Citations (1)
DOI: https://doi.org/10.31857/S2686954324010059
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.
Keywords: circulant graph, Laplacian matrix, eigenvalues, rooted spanning tree.
Funding agency Grant number
National Research Foundation of Korea 2018R1D1A1B05048450
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0005
The research of the first author was supported by the National Research Foundation of Korea (NRF) financed by the Ministry of Education, project no. 2018R1D1A1B05048450. The research of the second and third authors was performed within the state assignment of the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0005.
Presented: V. G. Romanov
Received: 21.04.2023
Revised: 19.01.2024
Accepted: 24.01.2024
English version:
Doklady Mathematics, 2024, Volume 109, Issue 1, Pages 25–29
DOI: https://doi.org/10.1134/S1064562424701771
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Y. S. Kwon, A. D. Mednykh, I. A. Mednykh, “On the structure of Laplacian characteristic polynomial of circulant graphs”, Dokl. RAN. Math. Inf. Proc. Upr., 515 (2024), 34–39; Dokl. Math., 109:1 (2024), 25–29
Citation in format AMSBIB
\Bibitem{KwoMedMed24}
\by Y.~S.~Kwon, A.~D.~Mednykh, I.~A.~Mednykh
\paper On the structure of Laplacian characteristic polynomial of circulant graphs
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 515
\pages 34--39
\mathnet{http://mi.mathnet.ru/danma489}
\crossref{https://doi.org/10.31857/S2686954324010059}
\elib{https://elibrary.ru/item.asp?id=67973246}
\transl
\jour Dokl. Math.
\yr 2024
\vol 109
\issue 1
\pages 25--29
\crossref{https://doi.org/10.1134/S1064562424701771}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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