Cayley Graphs with Complete Rotations

As it is introduced by Bermond, Pérennes, and Kodate and by Fragopoulou and Akl, some Cayley graphs, including most popular models for interconnection networks, admit a special automorphism, called complete rotation. Such an automorphism is often used to derive algorithms or properties of the underlying graph. For example, some optimal gossiping algorithms can be easily designed by using a complete rotation, and the constructions of the best known edge disjoint spanning trees in the toroidal meshes and the hypercubes are based on such an automorphism. Our purpose is to investigat- e such Cayley graphs. We relate some symmetries of a graph with potential algebraic symmetries appearing in its definition as a Cayley graph on a group. In the case of Cayley graphs defined on a group generated by transpositions, we characterize the ones admitting a complete rotation