Some lemmas on spectral radius of graphs: including an application

Fuente: arXiv
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Main Author: Zhang, Wenqian
Format: Preprint
Published: 2026
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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