A Comparative Study of Star Graphs and Rotator Graphs

Star graph is an extensively studied Cayley graph, considered to be an attractive alternative to the popular binary cube. The rotator graphs are a set of directed Cayley graphs introduced recently. In this paper we compare the structural and algorithmic aspects of star graphs with that of rotator graphs. In the process we present some new results for star graphs and rotator graphs. We present a formula for the number of nodes at any distance from the identity permutation in star graphs. The minimum bisection width of star and rotator graphs is obtained. Partitioning and fault tolerant parameters for both star and rotator graphs are analyzed. The node disjoint parallel paths and hence the upper bound on the fault diameter of rotator graphs are presented. We compare the minimal path routing in star and rotator graphs using simulation results.