Ordering of some uniform unicyclic hypergraphs with larger spectral radii

We study certain uniform unicyclic hypergraphs having larger spectral radii. For the uniform unicyclic hypergraphs, we first introduce the breadth-first-search ordering and then develop a new tool, namely the majorization theorem, to study their spectral radii. By using the technique obtained here, we deduce several new results. Firstly, we characterize the unique hypergraph with the largest spectral radius among the uniform unicyclic hypergraphs with a given degree sequence. Secondly, we provide simpler and shorter proofs for the first five hypergraphs with the largest spectral radii among Um and the hypergraph with the largest spectral radius among the uniform unicyclic hypergraphs with a given matching number, where Um is the set of the connected uniform unicyclic hypergraphs having m edges with m⩾8. Thirdly, we obtain the unique hypergraph with the largest spectral radius among the uniform unicyclic hypergraphs with a given maximum degree or a given number of pendent vertices.