| Summary: | 碩士 === 國立臺灣科技大學 === 資訊管理系 === 105 === Let G=(V,E) be an undirected graph, where V(G) and E(G) are vertex and edge sets of G, respectively. For simplicity, we also use V and E to represent V(G) and E(G), respectively. For any vertex vV , the open neighborhood of v is the set NG(v) = {uV : uv E}. The closed neighborhood of v is NG[v] = NG(v){v}. For simplicity, NG(v) and NG[v] are simply written as N(v) and N[v], respectively. A set D is a dominating set of a graph G if every vertex in V\D is adjacent to at least one vertex in D. The domination problem and its variants were extensively studied, e.g., independent domination, rainbow domination, total domination, roman domination, etc. We can find that all variants on the domination problem are adding some constraints to the domination problem. In this thesis, we investigate a new variant of the domination problem called the outer-paired domination problem which is defined as follows. An outer-paired domination set (OPD-set for short) of a graph G is a dominating set D of G such that the induced subgraph of V\D contains a perfect matching. In this thesis, we propose an O(n)-time algorithm for solving the outer-paired domination problem on proper interval graphs, where n is the number of vertices in V .
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