Concerning two conjectures on the set of fixed points of a complete rotation of a Cayley digraph Original Research Article

In 1996, J.C. Bermond, T. Kodate, S. Perennes and N. Marlin conjectured that the set Fσ of fixed points of some complete rotation σ of the toroidal mesh TM(p)k is not separating (that is Fσ does not disconnect TM(p)k). They also conjectured that the set Fω of fixed points of any complete rotation ω of any Cayley digraph is not separating. In this paper, we prove the first conjecture and disprove the second one.