On the spectra and the laplacian spectra of graphs

Abstract

Throughout all graphs are assumed to be simple Let A G and L G denote the adjacency and the Laplacian matrix corresponding to a graph G respectively The second smallest eigen value of L G is called the algebraic connectivity of G and is denoted by a G A corresponding eigenvector is called a Fiedler vector of G The study of spectral integral variations in graphs has been a subject of interest in the past few years see Fan 21 22 23 Kirkland 46 and So 65 We say that the spectr