The trace of uniform hypergraphs with application to Estrada index
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912490927947776 |
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| author | Fan, Yi-Zheng Zheng, Jian Yang, Ya |
| author_facet | Fan, Yi-Zheng Zheng, Jian Yang, Ya |
| contents | In this paper we investigate the traces of the adjacency tensor of hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and provide some perturbation results for the traces of a hypergraph with cut vertices. As applications we determine the unique hypertree with maximum Estrada index among all hypertrees with fixed number of edges and perfect matchings, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with fixed number of edges and girth $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03311 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The trace of uniform hypergraphs with application to Estrada index Fan, Yi-Zheng Zheng, Jian Yang, Ya Combinatorics Primary 05C65, 15A69, Secondary 13P15, 14M99 In this paper we investigate the traces of the adjacency tensor of hypergraphs (simply called the traces of hypergraphs). We give new expressions for the traces of hypertrees and linear unicyclic hypergraphs by the weight function assigned to their connected sub-hypergraphs, and provide some perturbation results for the traces of a hypergraph with cut vertices. As applications we determine the unique hypertree with maximum Estrada index among all hypertrees with fixed number of edges and perfect matchings, and the unique unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph with fixed number of edges and girth $3$. |
| title | The trace of uniform hypergraphs with application to Estrada index |
| topic | Combinatorics Primary 05C65, 15A69, Secondary 13P15, 14M99 |
| url | https://arxiv.org/abs/2210.03311 |