Topological properties and optimal routing algorithms for three dimensional hexagonal networks

The paper presents a convenient addressing scheme on 2D hexagonal meshes. It helps to derive simple and optimal routing and one-to-all broadcasting algorithms. We also show the existence of a Hamiltonian cycle that yields a ring embedding. We define 3D hexagonal graph as a generalization of the triangular plane tessellation, and consider it as a multiprocessor interconnection network. Some of its topological properties are studied. These properties are better than the well known multidimensional square mesh. A simple and optimal routing algorithm is also presented.