Expanding graphs, Ramanujan graphs, and 1-factor perturbations
نویسندگان
چکیده
We construct (k±1)-regular graphs which provide sequences of expanders by adding or substracting appropriate 1-factors from given sequences of kregular 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 6−2 √ 5 ≈ 1.52; the corresponding minoration for a sequence of Ramanujan 7-regular graphs (which is not known to exist) would be 7− 2 √ 6 ≈ 2.10.
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