The spectrum of the Corona of Hypergraphs
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910354021285888 |
|---|---|
| author | Kurian, Liya Jess A. V, Chithra |
| author_facet | Kurian, Liya Jess A. V, Chithra |
| contents | The corona of hypergraphs is an extension of the corona operation applied to graphs. The corona $G_0^* \odot_1^n G_1^*$ of two hypergraphs is obtained by taking $n$ copies of $G_1^*$ (where $n$ is the order of $G_0^*$) and by joining the $i$-th vertex of $G_0^*$ with the $i$-th copy of $G_1^*$. In this paper, we estimate the complete spectrum(adjacency and Seidel) and eigenvectors of the corona $G_0^* \odot_1^n G_1^*$ of two hypergraphs when $G_1^*$ is regular. Additionally, we define the corona hypergraph $G_0^{*(m)}=G_0^{*(m-1)} \odot_1^n G_0^*$ and determined its adjacency spectrum. Also, we extend the definition coronal of the adjacency matrix. Moreover, we estimate the characteristic polynomial of Seidel matrix of the generalised corona of hypergraphs. Applying these results, we obtain infinitely many non-regular non-isomorphic adjacency and Seidel cospectral hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The spectrum of the Corona of Hypergraphs Kurian, Liya Jess A. V, Chithra Combinatorics 05C65, 05C50, 15A18 The corona of hypergraphs is an extension of the corona operation applied to graphs. The corona $G_0^* \odot_1^n G_1^*$ of two hypergraphs is obtained by taking $n$ copies of $G_1^*$ (where $n$ is the order of $G_0^*$) and by joining the $i$-th vertex of $G_0^*$ with the $i$-th copy of $G_1^*$. In this paper, we estimate the complete spectrum(adjacency and Seidel) and eigenvectors of the corona $G_0^* \odot_1^n G_1^*$ of two hypergraphs when $G_1^*$ is regular. Additionally, we define the corona hypergraph $G_0^{*(m)}=G_0^{*(m-1)} \odot_1^n G_0^*$ and determined its adjacency spectrum. Also, we extend the definition coronal of the adjacency matrix. Moreover, we estimate the characteristic polynomial of Seidel matrix of the generalised corona of hypergraphs. Applying these results, we obtain infinitely many non-regular non-isomorphic adjacency and Seidel cospectral hypergraphs. |
| title | The spectrum of the Corona of Hypergraphs |
| topic | Combinatorics 05C65, 05C50, 15A18 |
| url | https://arxiv.org/abs/2403.02650 |