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Expanding graphs, Ramanujan graphs, and 1-factor perturbations

Pierre de la Harpe·Antoine Musitelli
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Abstract

We construct (k+-1)-regular graphs which provide sequences of expanders by adding or substracting appropriate 1-factors from given sequences of k-regular graphs. We compute numerical examples in a few cases for which the given sequences are from the work of Lubotzky, Phillips, and Sarnak (with k-1 the order of a finite field). If k+1 = 7, our construction results in a sequence of 7-regular expanders with all spectral gaps at least about 1.52.

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Pierre de la Harpe, Antoine Musitelli. 2005-03-16. Expanding graphs, Ramanujan graphs, and 1-factor perturbations. https://arxiv.org/abs/math/0503330

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