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Constructing Cospectral Hypergraphs Using Adjacency Preserving Permutations
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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BibTeX
@misc{das2026constructing,
title = {{Constructing Cospectral Hypergraphs Using Adjacency Preserving Permutations}},
author = {Arpita Das and Debjit Ghosal},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06199},
eprint = {2611.06199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06199},
}
RIS
TY - UNPB
TI - Constructing Cospectral Hypergraphs Using Adjacency Preserving Permutations
AU - Arpita Das
AU - Debjit Ghosal
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06199
UR - https://arxiv.org/abs/2611.06199
AB - 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 S_n 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.
ER -