On a cheeger type inequality in Cayley graphs of finite groups

2018/03/11 by Biswas, Arindam · 1 citation
#05C75 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1803.03969

Abstract

Let G be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph C(G,S) is an expander graph and is non-bipartite then the spectrum of the adjacency operator T is bounded away from -1. In this article we are interested in explicit bounds for the spectrum of these graphs. Specifically, we show that the non-trivial spectrum of the adjacency operator lies in the interval [-1+\frach(\mathbbG)⁴γ, 1-\frach(\mathbbG)²2d²], where h(\mathbbG) denotes the (vertex) Cheeger constant of the d regular graph C(G,S) with respect to a symmetric set S of generators and γ= 2⁹d⁶(d+1)².

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• Uniform expansion in finite groups of Lie type

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