The maximal spectral radius of the uniform unicyclic hypergraphs with perfect matchings

Abstract

Let U(n, k) and ?(n, k) be respectively the sets of the k-uniform connected linear and nonlinear unicyclic hypergraphs having perfect matchings with n vertices, where n ? k(k?1) and k ? 3. By using some techniques of transformations and constructing the incidence matrices for the hypergraphs considered, we get the hypergraphs with the maximal spectral radii among three kinds of hypergraphs, namely U(n, k) with n = 2k(k ? 1) and n ? 9k(k ? 1), ?(n, k) with n ? k(k ? 1), and U(n, k) ? ?(n, k) with n ? 2k(k ? 1), where k ? 3.