Ordering of $k$-uniform hypertrees by their distance spectral radii

Abstract

The distance spectral radius of a connected hypergraph is the largest
eigenvalue of its distance matrix. In this paper we present a new
transformation that decreases distance spectral radius. As applications, if $\Delta\geq\lceil\frac{m+1}{2}\rceil$, we determine the unique $k$-uniform hypertree of fixed $m$ edges and maximum degree $\Delta$ with the minimum distance spectral radius. And we characterize the $k$-uniform hypertrees on $m$ edges with the fourth, fifth, and sixth smallest distance spectral radius. In addition, we obtain the $k$-uniform hypertree on $m$ edges with the third largest distance spectral radius.