The maximum spectral radius of $θ_{2,2,3}$-free graphs with given size
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915213085769728 |
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| author | Gao, Jing Li, Xueliang |
| author_facet | Gao, Jing Li, Xueliang |
| contents | A theta graph $θ_{r,p,q}$ is the graph obtained by connecting two distinct vertices with three internally disjoint paths of length $r,p,q$, where $q\geq p\geq r\geq1$ and $p\geq2$. A graph is $θ_{r,p,q}$-free if it does not contain $θ_{r,p,q}$ as a subgraph. The maximum spectral radius of $θ_{1,p,q}$-free graphs with given size has been determined for any $q\geq p\geq2$. Zhai, Lin and Shu [Spectral extrema of graphs with fixed size: cycles and complete bipartite graphs, European J. Combin. 95 (2021) 103322] characterized the extremal graph with the maximum spectral radius of $θ_{2,2,2}$-free graphs having $m$ edges. In this paper, we consider the maximum spectral radius of $θ_{2,2,3}$-free graphs with size $m$ and characterize the extremal graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximum spectral radius of $θ_{2,2,3}$-free graphs with given size Gao, Jing Li, Xueliang Combinatorics 05C35, 05C50 A theta graph $θ_{r,p,q}$ is the graph obtained by connecting two distinct vertices with three internally disjoint paths of length $r,p,q$, where $q\geq p\geq r\geq1$ and $p\geq2$. A graph is $θ_{r,p,q}$-free if it does not contain $θ_{r,p,q}$ as a subgraph. The maximum spectral radius of $θ_{1,p,q}$-free graphs with given size has been determined for any $q\geq p\geq2$. Zhai, Lin and Shu [Spectral extrema of graphs with fixed size: cycles and complete bipartite graphs, European J. Combin. 95 (2021) 103322] characterized the extremal graph with the maximum spectral radius of $θ_{2,2,2}$-free graphs having $m$ edges. In this paper, we consider the maximum spectral radius of $θ_{2,2,3}$-free graphs with size $m$ and characterize the extremal graph. |
| title | The maximum spectral radius of $θ_{2,2,3}$-free graphs with given size |
| topic | Combinatorics 05C35, 05C50 |
| url | https://arxiv.org/abs/2503.19489 |