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arXiv · 2405.16839

On the Construction of Singular and Cospectral Hypergraphs

Liya Jess Kurian·Chithra A. V
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Abstract

In this paper, we define two operations, neighbourhood m-splitting hypergraph $NS_m(\mathscr{G}^*)$ and non-neighbourhood splitting hypergraph $NNS(\mathscr{G}^*)$, and obtain several properties of their adjacency spectrum. We also estimate the energies of $NS_m(\mathscr{G}^*)$ and $NNS(\mathscr{G}^*)$. Moreover, we introduce two new join operations on $k$-uniform hypergraphs: the neighbourhood splitting V-vertex join $\mathscr{G}_1^*\veebar \mathscr{G}_2^*$ and the S-vertex join $\mathscr{G}_1^*\barwedge \mathscr{G}_2^*$ of hypergraphs $\mathscr{G}_1^*$ and $\mathscr{G}_2^*$, 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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Liya Jess Kurian, Chithra A. V. 2024-05-27. On the Construction of Singular and Cospectral Hypergraphs. https://arxiv.org/abs/2405.16839

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