| Summary: | 碩士 === 國立臺灣科技大學 === 資訊管理系 === 90 === Honeycomb meshes are a variation of mesh networks. In this thesis, we focus on the honeycomb hexagon mesh that is a honeycomb mesh wirh hexagons. An induced dominating path is an induced path that dominates every vertex in a honeycomb hexagon mesh. By using a recursive algorithm, we can find an induced dominating path of a honeycomb hexagon mesh.
We find the relationship between an induced dominating path and the degree of every vertex in a honeycomb hexagon mesh HMt . Let t be the size of HMt. The number of vertices in HMt is equal to 6t^2. Then, we develop an algorithm for finding an induced dominating path of HMt . We prove that only one vertex is dominated by two vertices in the induced dominating path. The time complexity of our algorithm is Ο(n), where n is the number of vertices in HMt . We can also compute the length of the induced dominating path by the formula 3t^2＋3t-2. Meanwhile, the upper and lower bound of the path length are 9/2t^2+3/2t-1,3t^2+3(t/3)-1 , respectively.
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