Incrementally extensible hypercube networks and their fault tolerance

The incrementally extensible hypercube or IEH graph, a generalization of the hypercube, was introduced in [1]. It is shown that IEH graphs are incrementally extensible in steps of 1, optimally fault tolerant and its diameter is logarithmic in the number of nodes. Moreover, for any given number of nodes, the difference of the maximum and the minimum degree of a node in the graph is ≤ 1; i.e., the graph is almost regular. We also analyze these graphs in presence of node failures. We develop a fault tolerant routing algorithm which can compute a minimal path between two arbitrary nodes in an IEH graph in the presence of the maximum number of allowable faults. We also determine the fault diameter of the graph. Thus, we show that the IEH graphs, while they can be defined for any integer number of computing nodes, retain all the desirable properties of regular hypercubes including fault tolerance and a tight fault diameter.