Parallel processors are classified into two classes: shared-memory multiprocessors and distributed- memory multiprocessors. In the shared-memory system, processors communicate through a common memory unit. However, in the distributed multiprocessor system, each processor has its own memory unit and the communications among the processors are performed through an interconnection network. Thus, the interconnection topology plays an important role in the performance of these parallel systems. Recently, some new classes of interconnection networks, referred as Gaussian and Eisenstein- Jacobi networks, have been introduced. In this dissertation, we study the problem of finding the shortest node disjoint paths in the Gaussian and the Eisenstein-Jacobi networks. Moreover, we also describe how to generate edge disjoint Hamiltonian cycles in Eisenstein- Jacobi and Generalized Hypercube networks. Node disjoint paths are paths between any given source and destination nodes such that the paths have no common nodes except the endpoints. Similarly, edge disjoint Hamiltonian cycles are cycles in a given graph where each node is visited once and returns to the starting node and every edge is in at most one cycle.Keywords: Hamiltonian cycles, Disjoint paths, Parallel computing, Interconnection networ
