The largest α-spectral radius of the k-uniform unicyclic hypergraphs with perfect matchings

Abstract

Let G be a k-uniform hypergraph with k ⩾ 2 and 0 ⩽ α < 1. The α-spectral radius of G is the largest modulus of all the eigenvalues of Aα (G), where Aα (G) = αD(G) + (1-α)A(G) is the convex linear combination of D(G) and A(G) with D(G) and A(G) being the degree diagonal tensor and the adjacency tensor of G, respectively. Let U (n, k) be the set of the k-uniform unicyclic hypergraphs having perfect matchings with n vertices, where n ⩾ k(k-1) and k ⩾ 3. By using a creative method of the α-Perron vector and several techniques for studying the α-spectral radii of hypergraphs, such as the well-known Perron-Frobenius theorem, the moving-edge operation, and the 2-switch transformation, the hypergraph with the largest α-spectral radius is characterized among U (n, k), where n ⩾ k(k-1) and k ⩾ 3.