TY - JOUR

T1 - On the Structure of Laplacian Characteristic Polynomial of Circulant Graphs

AU - Kwon, Y. S.

AU - Mednykh, A. D.

AU - Mednykh, I. A.

N1 - 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.

PY - 2024/2

Y1 - 2024/2

N2 - 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.

AB - 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.

KW - Laplacian matrix

KW - circulant graph

KW - eigenvalues

KW - rooted spanning tree

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187184179&origin=inward&txGid=3fe078b963ec5e1641e22ecb9bb13d3f

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001180328000005

UR - https://www.mendeley.com/catalogue/dbbedcf6-d7ab-3389-ba4e-34913af0754b/

U2 - 10.1134/S1064562424701771

DO - 10.1134/S1064562424701771

M3 - Article

VL - 109

SP - 25

EP - 29

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -