Let λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph G. In this paper, we investigate the behavior on λ2(G) when the graph G 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.
Scopus Subject Areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Second smallest normalized Laplacian eigenvalue
- Unicyclic graph