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On the Construction of Singular and Cospectral Hypergraphs

2024/05/27 by Liya Jess Kurian, Kurian, Liya Jess, Chithra A. V +1
Mathematics · Engineering · #Tensor decomposition and applications #Sparse and Compressive Sensing Techniques #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2405.16839

Abstract

In this paper, we define two operations, neighbourhood m-splitting hypergraph NSm(\mathscrG^*) and non-neighbourhood splitting hypergraph NNS(\mathscrG^*), and obtain several properties of their adjacency spectrum. We also estimate the energies of NSm(\mathscrG^*) and NNS(\mathscrG^*). Moreover, we introduce two new join operations on k-uniform hypergraphs: the neighbourhood splitting V-vertex join \mathscrG1^*\veebar \mathscrG2^* and the S-vertex join \mathscrG1^*\barwedge \mathscrG2^* of hypergraphs \mathscrG1^* and \mathscrG2^*, and determine their adjacency spectrum. As an application, we obtain infinite families of singular hypergraphs and infinite pairs of non-regular non-isomorphic cospectral hypergraphs.

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