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Iterative Construction of Cayley Expander Graphs

2006
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Theory of Computing
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We construct a sequence of groups G n , and explicit sets of generators Y n ⊂ G n , such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G 1 is the alternating group A d , the set of even permutations on the elements {1, 2, . . . , d}. The group G n is the group of all even symmetries of the rooted d-regular tree of depth n. Our results hold for any large enough d. We also describe a finitely generated infinite group G ∞ with generating

doi:10.4086/toc.2006.v002a005
dblp:journals/toc/RozenmanSW06
fatcat:wzjdosx6onf6zj3h4sbtduext4