The first few unicyclic and bicyclic hypergraphs with largest spectral radii

A connected k-uniform hypergraph with n vertices and m edges is called r-cyclic if n=m(k−1)−r+1. For r=1 or 2, the hypergraph is simply called unicyclic or bicyclic. In this paper we investigate hypergraphs that attain largest spectral radii among all simple connected k-uniform unicyclic and bicyclic hypergraphs. Specifically, by using some edge operations, the formula on power hypergraph eigenvalues, the weighted incidence matrix and a result on linear unicyclic hypergraphs, we determined the first five hypergraphs with largest spectral radius among all unicyclic hypergraphs and the first three over all bicyclic hypergraphs.