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Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian
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作者 Jürgen Jost Raffaella mulas florentin münch 《Communications in Mathematics and Statistics》 SCIE 2022年第3期371-381,共11页
We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and onl... We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size n−1/2.With the same method,we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree,provided this is at most n−1/2. 展开更多
关键词 Spectral graph theory Normalized Laplacian Largest eigenvalue Sharp bounds
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