Spectral radius of r-uniform supertrees with perfect matchings

supertree is a connected and acyclic hypergraph. The set of r-uniform supertrees with n vertices and the set of r-uniform supertrees with perfect matchings on rk vertices are denoted by T-n and T-r,T-k, respectively. H. Li, J. Shao, and L. Qi [J. Comb. Optim., 2016, 32(3): 741-764] proved that the hyperstar S-n,S-r attains uniquely the maximum spectral radius in T-n. Focusing on the spectral radius in T-r,T-k, this paper will give the maximum value in T-r,T-k and their corresponding supertree.