Algebraic Connectivity and Degree Sequences of Trees

Tuerker Biyikoglu, Josef Leydold

Published 2008-10-06Version 1

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 non-decreasing on every path on non-pendant vertices starting at the characteristic set of the Fiedler vector.