2 problems

Let $\mathbb{P}_m(n)$ be the undirected prefix-reversal graph, which is $2n$-regular for $m>1$. A sequence of regular graphs is an expander family if there exists $\varepsilon>0$ s…

Let $P(2,n)$ denote the prefix-reversal graph with parameter $m=2$, and let $sp(G)$ be the difference between the largest and second-largest eigenvalues of the adjacency matrix of…