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.

令G为连通超图。G的距离谱半径为其距离矩阵的最大特征值。G的维纳指数被定义为G的每对无序顶点之间的距离之和。如果n  =  m ( k − 1) − 1，则具有n 个顶点和m条边的连通k -均匀超图G称为双环。首先，我们获得具有n个顶点的k -均匀双环超图 的维纳指数的下界。作为一个应用程序，在所有k- 具有n 个顶点的均匀双环超图，我们确定k ≥ 4时具有最小距离谱半径的前四个双环超图，以及k  = 3 时具有最小距离谱半径的双环超图。