### 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.

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