- PII
- 10.31857/S2686954324010059-1
- DOI
- 10.31857/S2686954324010059
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 515 / Issue number 1
- Pages
- 34-39
- 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
- Date of publication
- 15.11.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 52
References
- 1. Медных А.Д., Медных И.А. Об асимптотике и арифметических свойствах функции сложности циркулянтных графов // ДАН. 2018. Т. 479. Вып. 4. С. 363–367.
- 2. Grunwald L.A., Mednykh I.A. The number of rooted forests in circulant graphs // Ars Math. Contemp. 2022. Vol. 22. No. 4. #P4.10. doi: 10.26493/1855-3974.2029.01d
- 3. Медных А.Д., Медных И.А. Индекс Кирхгофа для циркулянтных графов и его асимптотика // ДАН. 2020. Т. 494. Вып. 1. С. 43–47.
- 4. Liu Xg., Zhou Sm. Spectral characterizations of propeller graphs // Electron. J. Linear Algebra. 2014. Vol. 27. P. 19–38. doi: 10.13001/1081-3810.1603
- 5. Liu Xg., Lu P. Laplacian spectral characterization of dumbbell graphs and theta graphs // Discrete Math. Algorithms Appl. 2016. Vol. 8. No. 2. 1650028. DOI: 10.1142/S1793830916500282
- 6. Neumaerker N. The arithmetic structure of discrete dynamical systems on the torus // PhD Thesis. Bielefeld: Univ. Bielefeld, 2012.
- 7. Прасолов В.В. Многочлены. М.: МЦНМО, 2003. 335 с.
- 8. Chebotarev P., Shamis E. Matrix forest theorem // arXiv:math/0602575. 2006.
- 9. Knill O. Cauchy-Binet for pseudo-determinants // Linear Algebra Appl. 2014. Vol. 459. P. 522–547. doi:10.1016/j.laa.2014.07.013
- 10. Kelmans A.K., Chelnokov V.M. A certain polynomial of a graph and graphs with an extremal number of trees // J. Comb. Theory Ser. B. 1974. Vol. 16. P. 197–214. doi: 10.1016/ 0095-8956(74)90065-3
