On the α-spectral radius of the k-uniform supertrees with perfect matchings

Let [Formula: see text] be a [Formula: see text]-uniform hypergraph with [Formula: see text]. The degree diagonal tensor and the adjacency tensor of [Formula: see text] are denoted by [Formula: see text] and [Formula: see text], respectively. Let [Formula: see text] be the convex linear combination of [Formula: see text] and [Formula: see text], where [Formula: see text]. The [Formula: see text]-spectral radius of [Formula: see text] is the largest modulus of all the eigenvalues of [Formula: see text]. A supertree is a connected and acyclic hypergraph. Let [Formula: see text] be the set of the [Formula: see text]-uniform supertrees having perfect matchings with [Formula: see text] vertices, where [Formula: see text] and [Formula: see text]. By using several useful transformations and some techniques for studying the [Formula: see text]-spectral radii of hypergraphs, the supertrees with the largest and the second largest [Formula: see text]-spectral radii are characterized among [Formula: see text], where [Formula: see text] and [Formula: see text].