The triangular pyramid: Routing and topological properties

In this paper, a new topology for multicomputer interconnection networks, based on triangular mesh, is proposed. The new network, referred to as the triangular pyramid (or tripy for short), has L levels of triangular mesh. We study some basic important properties of the proposed network as well as introduce a routing algorithm for the tripy network based on the routing of triangular meshes. We prove that this form of pyramidal network is Hamiltonian, Hamiltonian-connected, and pancyclic. We also prove that the proposed network is 6-colorable and conduct a brief comparison of the tripy and its traditional pyramid counterpart. Our results show that the proposed network has higher scalability, connectivity, and total network bandwidth while preserving the important properties of the traditional pyramid network.