Article ID Journal Published Year Pages File Type
419333 Discrete Applied Mathematics 2014 12 Pages PDF
Abstract

Let λ2(G)λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph GG. In this paper, we investigate the behavior on λ2(G)λ2(G) when the graph GG is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with λ2(G)≥1−22. Moreover, the trees and unicyclic graphs with λ2(G)=1−22 are also determined, respectively.

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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
Preview
An edge-separating theorem on the second smallest normalized Laplacian eigenvalue of a graph and its applications
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