BC Interconnection Networks and Their Properties

This paper proposes a family of interconnection networks called bijection connected (BC) graphs that properly contain the crossed cubes and the Mbius cubes and possess the same logarithm level diameters and node degrees, the highest connectivity (fault tolerance), and diagnosability as the hypercubes. Thus, this merges the study of some properties of the hypercube and a great many interconnection networks similar to it in structure. In addition, this paper proves that the BC interconnection network family contains a kind of Hamilton connected graphs and gives a guess on the diameters of the graphs in it.