Eigenvalues of the adjacency tensor on products of hypergraphs

Abstract

We consider the generalized notions of Cartesian and tensor products on m-uniform hypergraphs. The adjacency tensor is analogous to the adjacency matrix and two different notions of eigenvalues of the adjacency tensor on the products of hypergraphs are studied. The eigenvalues and E-eigenvalues of the adjacency tensor of the Cartesian and tensor products of two hypergraphs in relation to the E-eigenvalues and eigenvalues of the adjacency tensor of the factors are considered.