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.
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Funding
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.
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Translated by I. Ruzanova
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Kwon, Y.S., Mednykh, A.D. & Mednykh, I.A. On the Structure of Laplacian Characteristic Polynomial of Circulant Graphs. Dokl. Math. (2024). https://doi.org/10.1134/S1064562424701771
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DOI: https://doi.org/10.1134/S1064562424701771