ON THE SPECTRA OF TENSOR JOIN OF HYPERGRAPHS

In this paper, we consider certain classes of hypergraphs constructed from the tensor join of hypergraphs, specifically the tensor join of hypergraphs constrained by vertex subsets and the (H, \mathcal{T}_{\mathcal{S}})-join of hypergraphs constrained by \mathcal{S}. We determine some eigenvalues of the adjacency tensor of these classes of hypergraphs by establishing corresponding eigenvectors. We demonstrate that the eigenvalues of the adjacency tensor of the constituting hypergraphs are also eigenvalues of the adjacency tensor of the join of a set of hypergraphs. Furthermore, as a special case of our results, we provide some eigenvalues and eigenvectors of the adjacency tensor for the join of non-uniform hypergraphs on a backbone hypergraph H (and, similarly, for the join of m-uniform hypergraphs on a backbone hypergraph H). Additionally, we establish a relationship between the eigenvalues of the adjacency tensor of a hypergraph H and certain eigenvalues of the adjacency tensor of the (H, \mathcal{T}_{\mathcal{S}})-join of hypergraphs constrained by \mathcal{S}. Using this relationship, we determine some eigenvalues and their corresponding eigenvectors for the adjacency tensor of the lexicographic product of two hypergraphs.

کلیدواژه ها:

Hypergraphs ، Tensor join ، Adjacency tensor ، Eigenvalues