Vertex-transitivity and routing for Cayley graphs in GCR representations

Dense, symmetric graphs are good candidates for effective interconnection networks. Cayley graphs, formed by Borel subgroups, are the densest, symmetric graphs known for a range of diameters [1]. Every Cayley graph can be represented with integer node labels by transforming into another existing topology, Generalized Chordal Ring (GCR) [2]. However, generally speaking, GCR graphs are not fully symmetric. In this paper, we provide a framework for the formulation of the complete symmetry (or vertex-transitivity) of Cayley graphs in the integer domain of GCR representations. Successful realization of such formulation offers a simple, iterative routing algorithm that is capable of determining multiple, shortest paths between any source and destination pairs. An example from a Borel Cayley graph is used to illustrate this concept.