ABSTRACT
The graph embedding problem is a central issue in evaluating a network. The graph embedding problem asks whether the quest graph is a subgraph of a host graph, and an important benefit of the graph embeddings is that we can apply an existing algorithm for guest graphs to host graphs. This problem has attracted a burst of studies in recent years. Cycle networks and path networks are suitable for designing simple algorithms with low communication costs. The cycle embedding problem, which deals with all possible length of the cycles in a given graph, is investigated in a lot of interconnection networks [84,123,176,185,187,225,243]. The path embedding problem, which deals with all possible lengths of the paths between given two vertices in a given graph, is also investigated in a lot of interconnection networks [48,104-106,159,161,162,225,243,244,247]. In graph theory, we use the term pancyclic property to discuss the cycle embedding problem and the term panconnected property to discuss the path embedding problem.
