A characterization of spectral integral variation in two places for Laplacian matrices

Author: Steve Kirkland  

Publisher: Taylor & Francis Ltd

ISSN: 0308-1087

Source: Linear and Multilinear Algebra, Vol.52, Iss.2, 2004-03, pp. : 79-98

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We describe the graphs having the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing by 1 and the other Laplacian eigenvalues remaining fixed. For a certain subclass of graphs, we also characterize the Laplacian integral graphs with that property. Finally, we investigate a situation in which the algebraic connectivity is one of the eigenvalues that increases by 1.