TY - JOUR

T1 - Random Cayley graphs and expanders

AU - Alon, Noga

AU - Roichman, Yuval

PY - 1994/4

Y1 - 1994/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990704735&partnerID=8YFLogxK

U2 - 10.1002/rsa.3240050203

DO - 10.1002/rsa.3240050203

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AN - SCOPUS:84990704735

SN - 1042-9832

VL - 5

SP - 271

EP - 284

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 2

ER -