Random Cayley graphs and expanders

  • Authors:
  • Noga Alon;Yuval Roichman

  • Affiliations:
  • Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel;Department of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 1994

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Abstract

For every 1 δ 0 there exists a c = c(δ) 0 such that for every group G of order n, and for a set S of c(δ) log n random elements in the group, the expected value of the second largest eigenvalue of the normalized adjacency matrix of the Cayley graph X(G, S) is at most (1 ‐ δ). This implies that almost every such a graph is an ϵ(δ)‐expander. For Abelian groups this is essentially tight, and explicit constructions can be given in some cases. © 1994 John Wiley & Sons, Inc.