# Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

@article{Jost2019SpectralGO, title={Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian}, author={Jurgen Jost and Raffaella Mulas and Florentin M{\"u}nch}, journal={arXiv: Spectral Theory}, year={2019} }

We offer a new method for proving that the maximal eigenvalue of the normalized graph Laplacian of a graph with $n$ vertices is at least $\frac{n+1}{n-1}$ 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 $\frac{n-1}2$. 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 $\frac{n-1}{2…

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## 4 Citations

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