Some Topological Properties of the Honeycomb Rhombic Torus Based on Cayley Graph

Honeycomb tori are attractive alternatives to torus due to the smaller node degree, leading to lower complexity and lower implementation cost. The honeycomb networks are Cayley graphs with excellent topological properties. However, some topological properties of the honeycomb rhombic tori, such as internode distance, routing algorithm and broadcasting algorithm, are not developed. In this paper, we analyze the distance between any two nodes in the honeycomb rhombic tori and present an optimal routing algorithm for this class of networks. The algorithm is fully distributed, which can construct the shortest path between any pair of vertices. A broadcasting algorithm is also presented.