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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2406.07821 |
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| _version_ | 1866916757943353344 |
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| author | Zhang, Wenqian |
| author_facet | Zhang, Wenqian |
| contents | For a graph G, the spectral radius \r{ho}(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we seek the relationship between \r{ho}(G) and the walks of the subgraphs of G. Especially, if G contains a complete multi-partite graph as a spanning subgraph, we give a formula for \r{ho}(G) by using an infinite series on walks of the subgraphs of G. These results are useful for the current popular spectral extremal problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07821 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Walks, infinite series and spectral radius of graphs Zhang, Wenqian Combinatorics 05C50 For a graph G, the spectral radius \r{ho}(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we seek the relationship between \r{ho}(G) and the walks of the subgraphs of G. Especially, if G contains a complete multi-partite graph as a spanning subgraph, we give a formula for \r{ho}(G) by using an infinite series on walks of the subgraphs of G. These results are useful for the current popular spectral extremal problem. |
| title | Walks, infinite series and spectral radius of graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2406.07821 |