Embedding Augmented Cube into Certain Trees and Windmill Graphs

The technique used in studying the computational capabilities of interconnection networks and task distribution is graph embedding. Based on the recursively constructed graphs, the hypercube network is popular for its structure. Many variants of hypercube are considered in the literature. Augmented cube is considered as one of the best variants of hypercube as it holds many desirable properties like optimal routing in linear time complexity, vertex symmetricity, wide diameter and maximum connectivity. Our work deals with the exact wirelength, when augmented cube is embedded into certain tree and windmill structures.