Abstract: The talk is devoted to the investigation of the structure of characteristic polynomials of Laplaian matrix for a wide family of graphs admitting cyclic group action. As a result theorem describing analytical formula for respective polynomials are established. This allow us to do some more extensive analysis of various graph invariants. Namely the number of spanning trees, the number of rooted spanning forests, Kirchhoff index and some others.

Cite: Mednykh I.
Characteristic polynomial of Laplacian matrix for circulant foliations
International Conference and PhD-Master Summer School "Groups and Graphs, Algebras and Applications" 04-17 Aug 2025