Spectral radius of <Emphasis Type="Italic">r</Emphasis>-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,k, respectively. H. Li, J. Shao, and L. Qi J. Comb. Optim., 2016, 32(3): 741–764] proved that the hyperstar S_n,r attains uniquely the maximum spectral radius in T_n. Focusing on the spectral radius in T_r,k, this paper will give the maximum value in T_r,k and their corresponding supertree.