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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.00326 |
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| _version_ | 1866913592020828160 |
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| author | Cai, Yirong Deng, Hanyuan |
| author_facet | Cai, Yirong Deng, Hanyuan |
| contents | Let $P(G)=(P_{0}(G),P_{1}(G),\cdots, P_ρ(G))$ be the path sequence of a graph $G$, where $P_{i}(G)$ is the number of paths with length $i$ and $ρ$ is the length of a longest path in $G$. In this paper, we first give the path sequences of some graphs and show that the number of paths with length $h$ in a starlike tree is completely determined by its branches of length not more than $h-2$. And then we consider whether the path sequence characterizes a graph from a different point of view and find that any two graphs in some graph families are isomorphic if and only if they have the same path sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The path sequence of a graph Cai, Yirong Deng, Hanyuan General Mathematics Let $P(G)=(P_{0}(G),P_{1}(G),\cdots, P_ρ(G))$ be the path sequence of a graph $G$, where $P_{i}(G)$ is the number of paths with length $i$ and $ρ$ is the length of a longest path in $G$. In this paper, we first give the path sequences of some graphs and show that the number of paths with length $h$ in a starlike tree is completely determined by its branches of length not more than $h-2$. And then we consider whether the path sequence characterizes a graph from a different point of view and find that any two graphs in some graph families are isomorphic if and only if they have the same path sequence. |
| title | The path sequence of a graph |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2412.00326 |