The first two largest spectral radii of uniform supertrees with given diameter

A supertree is a connected and acyclic hypergraph. Let S(m,d,k) be the set of k-uniform supertrees with m edges and diameter d. In this paper, we determine the supertrees with the first two largest spectral radii among all supertrees in S(m,d,k) for 3≤d≤m−1.