Integral uniform hypergraphs

Abstract

In this paper we introduce the concept of integral hypergraphs - hypergraphs whose all adjacency eigenvalues are integers, in analogy to integral graphs. We present infinite families of integral uniform hypergraphs, especially hypergraphs built by two operations, the s-extension of a graph and the k-power of a graph. Our main result is about integrality for uniform hypercycles, obtaining a characterization of integral hypercycles in three specific cases: 3-uniform, 4-uniform and 5-uniform hypercycles. From these cases, a more general result is left open.