At the end of the spectrum: Chromatic bounds for the largest eigenvalue of the normalized Laplacian

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Abstract

For a graph with largest normalized Laplacian eigenvalue N and (vertex) coloring number, it is known that N / (-1). Here we prove properties of graphs for which this bound is sharp, and we study the multiplicity of / (-1). We then describe a family of graphs with largest eigenvalue / (-1). We also study the spectrum of the 1-sum of two graphs, with a focus on the maximal eigenvalue. Finally, we give upper bounds on N in terms of.

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Beers et al. (Wed,) studied this question.

synapsesocial.com/papers/68e79412b6db6435877052c2 https://doi.org/https://doi.org/10.48550/arxiv.2402.09160

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