Expanders from symmetric codes
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A new family of Cayley expanders (?)
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A combinatorial construction of almost-ramanujan graphs using the zig-zag product
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Symmetric LDPC codes and local testing
Property testing
Symmetric LDPC codes and local testing
Property testing
Finite groups and complexity theory: from leningrad to saint petersburg via las vegas
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
A Combinatorial Construction of Almost-Ramanujan Graphs Using the Zig-Zag Product
SIAM Journal on Computing
A key-distribution mechanism for wireless sensor networks using Zig-Zag product
International Journal of Ad Hoc and Ubiquitous Computing
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We consider the standard semi-direct product A 脳 B of finite groups A, B. We show that with certain choices of generators for these three groups, the Cayley graph of A 脳 B is (essentially) the zigzag product of the Cayley graphs of A and B. Thus, using the results of [RVW00], the new Cayley graph is an expander if and only if its two components are. We develop some general ways of using this construction to obtain large constant-degree expanding Cayley graphs from small ones.In [LW93], Lubotzky andWeiss asked whether expansion is a group property; namely, is being expander for (a Cayley graph of) a group G depend solely on G and not on the choice of generators. We use the above construction to answer the question in negative, by showingan infinite family of groups Ai 脳 Bi which are expanders with one choice of (constant-size) set of generators and are not with another such choice. It is interesting to note that this problem is still open, though, for "natural" families of groups, like the symmetric groups Sn or the simple groups PSL(2, p).