arXiv subjects
Publications and source records attributed to Rong-Ying Pan.
In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.
The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the graph Laplacian for given a degree sequence, the Laplacian coefficients, the algebraic connectivity and the graph doubly stochastic matrix, and the spectra of random graphs and the small world networks. In addition, some questions are proposed.