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Examples of 3-transitive expander family of Schreier graphs

What are examples of expander family of 3-transitive Schreier graphs? Meaning for an action that is 3-transitive. It is better to have an option for randomization. We know that choosing 2 elements ...
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Expander graphs with many 4-cycles

The question is not strictly well-defined. But it goes like this: Could you find an infinite family of graphs $G_i$, that are all $\epsilon$-expanders, but have many 4-cycles? $\epsilon$ should ...
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