Expanding graphs, Ramanujan graphs, and 1-factor perturbations
组合数学
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0503330,
title = {Expanding graphs, Ramanujan graphs, and 1-factor perturbations},
author = {Pierre de la Harpe and Antoine Musitelli},
journal= {arXiv preprint arXiv:math/0503330},
year = {2007}
}