Algebraic degree of spectra of Cayley hypergraphs

Let (G, .) be a finite group with the identity e and S a subset of G\{e} such that S = S-1. For t is an element of N and 2 <= t <= max{o(x) : x is an element of S}, the t-Cayley hypergraph of G over S is the hypergraph whose vertex set is G and edge set is {{yx(i) : 0 <= i <= t - 1} : x is an element of S and y is an element of G}. In this work, we study spectral properties of this hypergraph. We characterize integral 2-Cayley hypergraphs of G when G is abelian. In addition, we obtain the algebraic degree of t-Cayley hypergraphs of Z(n). (C) 2022 Elsevier B.V. All rights reserved.