Maximum and minimum nullity of a tree degree sequence

Gonzalo Molina, Daniel A. Jaume

Published 2018-06-06Version 1

The nullity of a graph is the multiplicity of the eigenvalue zero in its adjacency spectrum. In this paper, we give a closed formula for the minimum and maximum nullity among trees with the same degree sequence, using the notion of matching number and annihilation number. Algorithms for constructing such minimum-nullity and maximum-nullity trees are described.