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arXiv · 1910.14402

Spectral gap of the largest eigenvalue of the normalized graph Laplacian

Jürgen Jost·Raffaella Mulas·Florentin Münch
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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 $\frac{n+1}{n-1}$ 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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Jürgen Jost, Raffaella Mulas, Florentin Münch. 2019-10-31. Spectral gap of the largest eigenvalue of the normalized graph Laplacian. https://doi.org/10.1007/s40304-020-00222-7

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