Algebraic Connectivity and Degree Sequences of Trees

Details Algebraic Connectivity and Degree Sequences of Trees Algebraic Connectivity and Degree Sequences of Trees

2008-10-06

arxiv.org/abs/0810.0966v1

Mathematics

Combinatorics

8 pages

Scientific paper

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.

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