Embedding De Bruijn, Kautz and Shuffle-exchange Networks in Books

We show that the de Bruijn digraph B(d, D), D > 1 and the Kautz digraph K(d, D) can be embedded in (d + 1) pages with cumulative pagewidth 14dD − 2(3d3 − 2d2 + 4d − d(d mod 2) − 4) and 14dD − 1(3d2 + 4d + (d mod 2)), respectively. Also we show that the shuffle-exchange graph S(D), D > 2 can be embedded in 3 pages with cumulative pagewidth 5 ·2D − 3. From these results, the pagenumbers of B(2, D), K(2, D) and S(D) are determined to be 3.