# Constructing Cospectral Hypergraphs Using Adjacency Preserving Permutations

“Constructing Cospectral Hypergraphs Using Adjacency Preserving Permutations” (2026), by Das Arpita et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Das Arpita, Debjit Ghosal
- Published: November 4, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.06199
- Free PDF: https://arxiv.org/pdf/2611.06199

## Abstract

In this paper, we use permutations of the vertices of hypergraphs that preserve their adjacency matrices defined in banerjee 2021. These permutations form a group which lies between the automorphism group and the full symmetric group Sₙ where n is the number of vertices. Using elements from that group which are not automorphisms, we construct cospectral non-isomorphic hypergraphs. We use hypergraph structure coming from finite projective planes to show existence of infinitely many families of such hypergraphs. Also this method is very specific to uniform hypergraphs with uniformity greater than or equal to 3, i.e not applicable to graphs.

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