Some lemmas on spectral radius of graphs: including an application
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910052312416256 |
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| author | Zhang, Wenqian |
| author_facet | Zhang, Wenqian |
| contents | For a graph $G$, the spectral radius $ρ(G)$ of $G$ is the largest eigenvalue of its adjacency matrix. In this paper, we give three lammas on $ρ(G)$ when $G$ contains a spanning complete bipartite graph. Using these lemmas and typical spectral method, we characterized the unique extremal graph with the maximum spectral radius among all planar graphs of large order $n$ without a cycle of length $\ell$, where $5\leq \ell\leq n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some lemmas on spectral radius of graphs: including an application Zhang, Wenqian Combinatorics For a graph $G$, the spectral radius $ρ(G)$ of $G$ is the largest eigenvalue of its adjacency matrix. In this paper, we give three lammas on $ρ(G)$ when $G$ contains a spanning complete bipartite graph. Using these lemmas and typical spectral method, we characterized the unique extremal graph with the maximum spectral radius among all planar graphs of large order $n$ without a cycle of length $\ell$, where $5\leq \ell\leq n$. |
| title | Some lemmas on spectral radius of graphs: including an application |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.00621 |