On the Construction of Singular and Cospectral Hypergraphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909211202420736 |
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| author | Kurian, Liya Jess A. V, Chithra |
| author_facet | Kurian, Liya Jess A. V, Chithra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Construction of Singular and Cospectral Hypergraphs Kurian, Liya Jess A. V, Chithra Combinatorics 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. |
| title | On the Construction of Singular and Cospectral Hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.16839 |