ABSTRACT
Due to technological advances, multiprocessor systems with an increasing number of interconnected computing nodes are becoming a reality. The underlying topology of such a system is an interconnection network. Computing nodes can be processors in which the resulting system is a multiprocessor supercomputer, or they can be computers in which the resulting system is a computer network. This interconnection network can be represented by a graph. The chapter considers the relationships between super connectedness and other parameters, including several resiliency/vulnerability parameters, via sufficient conditions, that is, how super connectedness implies other parameters. The class of star graphs is a popular class of interconnection networks and it serves as a competitive model to the class of hypercubes. One may wonder whether these sufficient conditions are too strong. Perhaps they are too strong for graphs in general. However, interconnection networks have good “structural” properties. For interconnection networks, these sufficient conditions give many useful results.
