On distance spectral radius of trees with fixed maximum degree

Abstract

We determine the unique trees with minimum distance spectral radius
in the class of all trees on $n$ vertices with a fixed maximum
degree bounded below by $\lceil\frac{n}{2}\rceil$, and in the class
of all trees on $2m$ vertices
with perfect matching and a fixed maximum degree bounded below by $\lceil\frac{m}{2}\rceil+1$. We also determine the unique tree with
maximum distance spectral radius in the class of all trees on $2m$ vertices with perfect matching and a fixed maximum degree.