E-cospectral hypergraphs and some hypergraphs determined by their spectra

Two k-uniform hypergraphs are said to be cospectral (E-cospectral), if their adjacency tensors have the same characteristic polynomial (E-characteristic polynomial). A k-uniform hypergraph H is said to be determined by its spectrum, if there is no non-isomorphic k-uniform hypergraph cospectral with H. In this note, we give a method for constructing E-cospectral hypergraphs, which is similar with Godsil–McKay switching. Some hypergraphs are shown to be determined by their spectra.