| Summary: | 碩士 === 國立臺灣科技大學 === 資訊管理系 === 90 === Let u and v be two vertices in a simple graph G=(V,E), where V and E are the vertex and edge, respectively, sets of G. We say that u k-dominates v if their distance is less than or equal to k. A subset D of V is called a k-dominating set of G if for every vertex v in V there exists some vertex u in D which k-dominates v. If the cardinality of D is minimum among all k-dominating sets, then is said to be the minimum k-domination number, denoted γk(G), of G. The k-bondage number of G, bk(G), is the number of edges whose removed results in γk(G-S)＞γk(G), where S is the set of edges.
In this thesis, we are focus on finding the minimum k-domination number and the k-bondage number of paths, cycles and grid graphs P2×Pn .
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