Spanning trees in directed circulant graphs and cycle power graphs

The number of spanning trees in a class of directed circulant graphs with generators depending linearly on the number of vertices $\beta n$, and in the $n$-th and $(n-1)$-th power graphs of the $\beta n$-cycle are evaluated as a product of $\lceil \beta \mathrm{/}2\rceil -1$ terms.