Brualdi-Hoffman-Turán problem of the gem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915017439313920 |
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| author | Chen, Fan Yuan, Xiying |
| author_facet | Chen, Fan Yuan, Xiying |
| contents | A graph is said to be $F$-free if it does not contain $F$ as a subgraph. Brualdi-Hoffman-Turán problem seeks to determine the maximum spectral radius of an $F$-free graph with given size. The gem consists of a path on $4$ vertices, along with an additional vertex that is adjacent to every vertex of the path. Concerning Brualdi-Hoffman-Turán problem of the gem, when the size is odd, Zhang and Wang [Discrete Math. 347 (2024) 114171] and Yu, Li and Peng [arXiv:2404. 03423] solved it. In this paper, we completely solve the Brualdi-Hoffman-Turán problem type problem of the gem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brualdi-Hoffman-Turán problem of the gem Chen, Fan Yuan, Xiying Combinatorics A graph is said to be $F$-free if it does not contain $F$ as a subgraph. Brualdi-Hoffman-Turán problem seeks to determine the maximum spectral radius of an $F$-free graph with given size. The gem consists of a path on $4$ vertices, along with an additional vertex that is adjacent to every vertex of the path. Concerning Brualdi-Hoffman-Turán problem of the gem, when the size is odd, Zhang and Wang [Discrete Math. 347 (2024) 114171] and Yu, Li and Peng [arXiv:2404. 03423] solved it. In this paper, we completely solve the Brualdi-Hoffman-Turán problem type problem of the gem. |
| title | Brualdi-Hoffman-Turán problem of the gem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.08345 |