The spectral radius of the weighted k–uniform supertrees

Source abstract

The majorization theorem for the spectral radii of the weighted [Formula: see text]-uniform supertrees is developed. By applying the majorization theorem, we characterize the weighted hypergraphs with the maximum spectral radii among [Formula: see text] and [Formula: see text], and obtain the weighted hypergraphs with the first to the third maximum spectral radii among [Formula: see text], where [Formula: see text] denotes the collection of the weighted [Formula: see text]-uniform supertrees of order [Formula: see text] with positive integer weights and a fixed total weight sum [Formula: see text] for [Formula: see text] and [Formula: see text], [Formula: see text] the subset of [Formula: see text] in which each supertree has a given degree sequence [Formula: see text], and [Formula: see text] the subset of [Formula: see text] in which each supertree has a fixed weight set [Formula: see text] with [Formula: see text] and [Formula: see text]. In addition, an exact relationship between the spectral radii of a weighted graph and its weighted [Formula: see text]th power hypergraph is proved, where [Formula: see text].