On the Hamiltonicity, Connectivity, and Broadcasting Algorithm of the KCube

The KCube is a newly proposed topology for connecting many processors in an interconnection or communication network. It combines the well known Kautz graph and the hypercube. The KCube is defined in such a way that it is a class of graphs that have to satisfy two conditions for a graph to be a KCube. Therefore, different versions of the KCube are possible depending on how input and output nodes (vertices) are defined. Originally, together with the definition of the KCube family, a specific version of the KCube is also presented. In this paper, we (1) propose a KCube graph that also belongs to the KCube family and is yet different from the original one, study some of the properties of our KCube, and show that it is Hamiltonian, (2) derive its connectivity, and (3) develop an optimal broadcasting algorithm. The results in (2) and (3) are for the general KCube family regardless of how input and output nodes are specified.