On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph
نویسندگان
چکیده
Let G be a simple connected graph with order n. $$\mathcal{L}(G)$$ and $$\mathcal{Q}(G)$$ the normalized Laplacian signless matrices of G, respectively. λk(G) k-th smallest eigenvalue G. Denote by ρ(A) spectral radius matrix A. In this paper, we study behaviors λ2(G) $$\rho(\mathcal{L}(G))$$ when is perturbed three operations. We also properties X for bipartite graphs, where unit eigenvector corresponding to . Meanwhile characterize all graphs $$\rho(\mathcal{L}(G))=\rho(\mathcal{Q}(G))$$
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*Correspondence: [email protected] 1School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, P.R. China 2Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, P.R. China Full list of author information is available at the end of the article Abstract Let G be a simple connected graph of order n, where n≥ 2. Its normalized Laplacian eigenvalues are 0 = λ1 ...
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ژورنال
عنوان ژورنال: Acta Mathematicae Applicatae Sinica
سال: 2021
ISSN: ['0168-9673', '1618-3932']
DOI: https://doi.org/10.1007/s10255-021-1032-x