| Summary: | 博士 === 國立交通大學 === 資訊科學與工程研究所 === 100 === From the application point of view, efficient algorithms and execution methods are important issues for communication patterns in networks. The study of certain topological structures on network designs provides a systematic and logical analysis for the desired performance. The problem of simulating a network by another is called embedding problem. The cycle-embedding problem is one of the most popular research problems.
In this dissertation, we will introduce the bipancyclic property, bipanpositionable property, and bipanpositionable bipancyclic property, and show that some interconnection networks satisfy those properties. We also study the existence of mutually independent cycles on some interconnection networks. The existence of mutually independent cycles in communication system guarantees that there will be no waiting time for parallel processing. We propose a sufficient condition to guarantee the existence of certain number of mutually independent hamiltonian cycles. We also find the optimal number of mutually independent hamiltonian cycles in some special interconnection networks. Finally, we will introduce two new concepts called mutually independent edge-bipancyclic property and mutually independent bipanconnected property. Our result strengthens previous results such as bipancyclic property, bipanconnected property, edge-bipancyclic property, and vertex-bipancyclic property.
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