Cycles in the Cycle Prefix Digraph

Cycle prefix digraphs are a class of Cayley coset graphs with many remarkable properties, such as:Symmetry Large number of nodes for a given degree and diameter Simple shortest path routing Hamiltonicity Optimal connectivity Others.
In this paper, we show that the cycle prefix digraphs, like the Kautz digraphs, contain cycles of all lengths \(l\), with \(l\) between two and \(N\), the order of the digraph, except for \(N-1\).