Zig-zag product
In graph theory, the zig-zag product of regular graphs G , H {\displaystyle G,H} , denoted by G ∘ H {\displaystyle G\circ H} , is a binary operation which takes a large graph ( G {\displaystyle G} ) and a small graph ( H {\displaystyle H} ) and produces a graph that approximately inherits the size of the large one but the degree of the small one. An important property of the zig-zag product is that if H {\displaystyle H} is a good expander, then the expansion of the resulting graph is only slightly worse than the expansion of G {\displaystyle G} .