Integral uniform hypergraphs

Lucas Portugal and Renata Del-Vecchio

Applied Mathematics and Computation, 2025, vol. 504, issue C

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.

Keywords: Adjacency matrix; Spectrum; Integral hypergraph (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:504:y:2025:i:c:s0096300325002334

DOI: 10.1016/j.amc.2025.129507

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