Embedding an architecture in another is useful in providing architectural abstraction between different topologies. Through such embeddings the algorithms originally developed in one architecture can be directly mapped to another architecture.
Recently a new topology of interconnection networks, called recursive circulant, was proposed by Park and Chwa[Par92]. This paper presents a novel strategy for embedding in recursive circulants. By using this method, we present optimal one-to-one embeddings of cube-connected cycle, n-dimensional torus, and mesh of trees into recursive circulants.
Some interesting problems related on graph embedding are also considered. We analyze the maximal size of a hypercube that can be a subgraph of recursive circulants. And we find that some classes of graphs cannot be contained in any size of d-edge graphs. Especially recursive circulant itself is not a subgraph of d-edge graphs. This result implies that the d-edge labeling, proposed by Lim and Chwa[Lim93], has a limitation for a embedding method of recursive circulants by nature.
