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 -