| Summary: | 碩士 === 國立暨南國際大學 === 資訊工程學系 === 92 === With the development of network and parallel computers, the problems of interconnection network are more and more important. How do we make the efficiency to be optimal and how to reduce the cost are main goals of there problems. The properties of Cayley graph are very useful in the application of interconnection networks. Up to now, the related papers are still published frequently.
T-coloring problem is extended from coloring problem. The problem usually be applied in communication. For many different radio stations, their frequency may be interfere to each other because of their distance or other reasons. How to assign the frequency for every station such that make the cost are as less as possible is the most important for this problem.
In this thesis, we combine these two problems then discuss T-coloring problem on some Cayley graphs. It can be applied on the problems of communication of different hardware or computers in interconnection network. We discuss T-span and T-edge span for four kinds of T sets on fourteen different Cayley graphs in this thesis. We divide the results into three parts: in first part, we have find optimal solutions for some Cayley graph which are bipartite graphs or χ-perfect graphs. For Cayley graphs in second part, the structure of these Cayley graphs seems to be complex, but we still find optimal solutions for T-span and T-edge span except for T3-edge span. And for Cayley graphs in third part, although the structure of these Cayley graphs are more complex, we still find a lower bound and upper bound for T-span and T-edge span for three types Cayley graphs in this part.
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