Some remarks on Laplacian eigenvalues of connected graphs

Let G be a connected undirected graph with n vertices and m edges, and let μ1≥μ2≥…≥μn−1>μn=0 be Laplacian eigenvalues of adjacency matrix of G. In this paper a generalization of some inequalities for the Laplacian spreads LS(G)=μ1−μn−1, LR+(G)=μ1μn−1+μn−1μ1 and LR−(G)=μ1μn−1−μn−1μ1 is presented....

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Bibliographic Details
Published in:Linear algebra and its applications 2016-08, Vol.503, p.48-55
Main Authors: Jovanović, Z., Milovanović, E.I., Milovanović, I.Ž.
Format: Article
Language:English
Subjects:
Laplacian eigenvalues
Linear Laplacian spread
Ratio Laplacian spread
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Summary:Let G be a connected undirected graph with n vertices and m edges, and let μ1≥μ2≥…≥μn−1>μn=0 be Laplacian eigenvalues of adjacency matrix of G. In this paper a generalization of some inequalities for the Laplacian spreads LS(G)=μ1−μn−1, LR+(G)=μ1μn−1+μn−1μ1 and LR−(G)=μ1μn−1−μn−1μ1 is presented.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.03.046