Distance spectral radii of k-uniform bicyclic hypergraphs

Let G be a connected hypergraph. The distance spectral radius of G is the largest eigenvalue of its distance matrix. The Wiener index of G is defined to be the sum of distances between every unordered pair of vertices of G. A connected k-uniform hypergraph G with n vertices and m edges is called bicyclic if n = m(k − 1) − 1. Firstly, we obtain a lower bound on the Wiener index of k-uniform bicyclic hypergraphs with n vertices. As an application, among all k-uniform bicyclic hypergraphs with n vertices, we determine the first four bicyclic hypergraphs with smallest distance spectral radii for k ≥ 4, and the bicyclic hypergraph with minimum distance spectral radius for k = 3.