A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory

@article{Fiedler1975APO,
title={A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory},
author={Miroslav Fiedler},
journal={Czechoslovak Mathematical Journal},
year={1975},
volume={25},
pages={619-633}
}

We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are… Expand

It is proved that the standard spectral graph bisection can produce bisections that are far from optimal, and it is shown that the maximum error in the spectral approximation of the optimal bisection (partition sizes exactly equal) cut for such graphs is bounded below by a constant multiple of the order of the graph squared.Expand