2024/05/02 by Anirban Banerjee, Banerjee, Anirban, Samiron Parui +1
Engineering · #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2405.01364
This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism f, an \( f \)-compatible matrices capture aspects of the symmetry, represented by \( f \), within the hypergraph. First, we explore rotation, a specific kind of automorphism and find that the spectrum of any matrix compatible with a rotation can be decomposed into the spectra of smaller matrices associated with that rotation. We show that the spectrum of any \(f\)-compatible matrix can be decomposed into the spectra of smaller matrices associated with the component rotations comprising \( f \). Further, we study a hypergraph symmetry termed unit-automorphism, which induces bijections on the hyperedges, though not necessarily on the vertex set. We show that unit automorphisms also lead to the spectral decomposition of compatible matrices.