Properties of the Laplacian spectra of certain basic and hierarchical graphs
Victiria Erofeeva, Sergei Parsegov
The study of spectra of Laplacian matrices is important in decentralized optimization and multi-agent control problems. Namely, the largest and the smallest nonzero eigenvalues significantly affect both the stability of decentralized algorithms and their convergence rate. In this paper, we study the Laplacian spectra of some basic graphs and hierarchical graphs obtained from them. Explicit expressions for the eigenvalues of interest are given and analyzed.
CYBERNETICS AND PHYSICS, VOL. 13, NO. 1, 2024, 12–19
https://doi.org/10.35470/2226-4116-2024-13-1-12-19