A Class of Arc-Transitive Cayley Graphs as Models for Interconnection Networks

We study a class of Cayley graphs as models for interconnection networks. With focus on efficient communication we prove that for any graph in the class there exists a gossiping protocol which exhibits attractive features, and moreover we give an algorithm for constructing such a protocol. In particular, these hold for two important subclasses of graphs, namely, Cayley graphs admitting a complete rotation and Frobenius graphs of a certain type. For such Frobenius graphs, we obtain the minimum gossip time and give an optimal gossiping protocol under which messages are transmitted along shortest paths and each arc is used exactly once at each time step. Moreover, for such Frobenius graphs we construct an all-to-all routing which is a shortest path routing, arc-transitive, edgeand arc-uniform, and optimal for the edgeand arc-forwarding indices simultaneously.