| Summary: | 碩士 === 國立嘉義大學 === 資訊工程研究所 === 91 === The bandwidth of a graph is the minimum of the maximum difference between labels of adjacent vertices in the graph. Bandwidth of graphs is an useful parameter for many applications including solving linear equations, parallel computation network, VLSI layout problem, back tracing in the constraint satisfaction problem etc. If we label the edges instead of the vertices of the graph, we can define the edge-bandwidth accordingly. The edge-bandwidth of a graph is the minimum of the maximum difference between labels of adjacent edges in the graph. The edge-bandwidth problem is a restricted version of the bandwidth problem. Establishing the bandwidth of a line graph is equivalent to verifying the edge-bandwidth of one or more graphs. However, the computing complexity of the edge-bandwidth is unknown up to now. Another parameter which is related to bandwidth is called cyclic bandwidth of a graph. The application about the cyclic bandwidth is also in the area of parallel computation network and VLSI layout. It is known that the decision problems corresponding to finding the bandwidth and the cyclic bandwidth of an arbitrary graph are NP-complete. In this thesis we solved bandwidth, edge-bandwidth and cyclic bandwidth for some classes of graphs with extensive proof.
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