On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues |
| |
Affiliation: | School of Mathematical Sciences, MOE-LSC, SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, PR China |
| |
Abstract: | For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the (where ) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when , the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs. |
| |
Keywords: | Weighted spectral radius Unraveled ball Alon–Boppana bound Normalized Laplacian eigenvalue Weighted graph |
本文献已被 ScienceDirect 等数据库收录! |
|