Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 3 2026 06 01 ON THE SPECTRA OF TENSOR JOIN OF HYPERGRAPHS 489 508 3829 10.22044/jas.2025.14919.1880 EN Vishnupriya Ramkumar Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram–624 302, Tamil Nadu, India. Rajkumar Rajendran Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram–624 302, Tamil Nadu, India. Journal Article 2024 08 09 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. https://jas.shahroodut.ac.ir/article_3829_2f5badf8e43df6dcb8fdeb21c46e7cb8.pdf