~chitecture for Parallel Systems Upp Graphs A~d Uf\1fa Networks- Architecture for Parallel Systems

A graph with unique path property (UPP) has 211 vertices and a unique path of length n between each two vertices. These graphs are very important in the design of architectures and algorithms for interconnection netwp.rks. Given two UPP graphs we introduce an algorithm to determine 'isomorphisrp. betwe,en the graphs. We give two different cpnstructions 2"+1-311-2 for nonisdmorphic UPP graphs'and show a lower bound of 2 9 nonisomorphic graphs with 211 vertices. UMFA (Uniform Minimal Full Access) networks are multistage interconnection networks, that llse the same interconnection pattern between each two consecutive stages. These networks are derived from UPP graphs, and the most known net,:, work of this type is the Omega network. We deal with the problem of rearrangeability of UMFA networks. T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 51 8 19 88 2.