A Unified Addressing Schema for Hexagonal and Honeycomb Networks with Isomorphic Cayley Graphs

As interconnection architectures, the regular six-degree hexagonal networks and the regular three-degree honeycomb networks have been widely investigated. For the lack of a proper addressing schema, some published routing algorithms are very complicated and the topological properties of some complex hexagonal and honeycomb related architectures are not well known. In this paper, a unified addressing schema for hexagonal and honeycomb meshes is proposed; two Cayley graphs isomorphic to the two meshes are presented as a formal foundation for the addressing schema. Using the suggested addressing schema, simple distance formulas and concise shortest-path routing algorithms of the two meshes are developed. The routing algorithms may be directly applied in real interconnection networks such as cellular networks. The models based on the unified addressing schema and the two isomorphic Caylay graphs established a concise and elegant foundation to investigate complex hexagonal and honeycomb related networks