A Brualdi-Hoffman-Turán problem for friendship graph
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909322044243968 |
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| author | Chen, Fan Yuan, Xiying |
| author_facet | Chen, Fan Yuan, Xiying |
| contents | A graph is said to be $H$-free if it does not contain $H$ as a subgraph. Brualdi-Hoffman-Turán type problem is to determine the maximum spectral radius of an $H$-free graph $G$ with give size $m$. The $F_k$ is the graph consisting of $k$ triangles that intersect in exactly one common vertex, which is known as the friendship graph. In this paper, we resolve a conjecture (the Brualdi-Hoffman-Turán-type problem for $F_k$) of Li, Lu and Peng [Discrete Math. 346 (2023) 113680] by using the $k$-core technique presented in Li, Zhai and Shu [European J. Combin, 120 (2024) 103966]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Brualdi-Hoffman-Turán problem for friendship graph Chen, Fan Yuan, Xiying Combinatorics A graph is said to be $H$-free if it does not contain $H$ as a subgraph. Brualdi-Hoffman-Turán type problem is to determine the maximum spectral radius of an $H$-free graph $G$ with give size $m$. The $F_k$ is the graph consisting of $k$ triangles that intersect in exactly one common vertex, which is known as the friendship graph. In this paper, we resolve a conjecture (the Brualdi-Hoffman-Turán-type problem for $F_k$) of Li, Lu and Peng [Discrete Math. 346 (2023) 113680] by using the $k$-core technique presented in Li, Zhai and Shu [European J. Combin, 120 (2024) 103966]. |
| title | A Brualdi-Hoffman-Turán problem for friendship graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.14138 |