Zig-zag product

In graph theory, the zig-zag product of regular graphs ${\displaystyle G,H}$, denoted by ${\displaystyle G\circ H}$, takes a large graph (${\displaystyle G}$) and a small graph (${\displaystyle H}$), 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 ${\displaystyle H}$ is a good expander, then the expansion of the resulting graph is only slightly worse than the expansion of ${\displaystyle G}$.

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