Spectral gap of the largest eigenvalue of the normalized graph Laplacian

Jürgen Jost, Raffaella Mulas, and Florentin Münch

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Submission date: 13. Jan. 2020
Pages: 10
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Link to arXiv: See the arXiv entry of this preprint.

Abstract:
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 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 . 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 .