| Summary: | 碩士 === 國立東華大學 === 資訊工程學系 === 105 === The node searching problem on a graph G is to determine the minimum number of searchers to clear G via rules of node searching. This minimum number is called the node-search number of G. The node searching spanning tree problem on graph G is to find a spanning tree T of G such that the node-search number of T is the minimum among all possible spanning trees of G. In this thesis, we study the node searching spanning tree problem on unicyclic graphs. A unicyclic graph is a tree with an additional edge. That is, a unicyclic graph contains only one cycle. It is known that the node searching problem on trees can be solved in O(n) time, where n is the number of vertices in the tree. Thus, a straightforward algorithm for solving the node searching spanning tree problem on unicyclic graphs runs in O(n2) time. In this study, we present a linear-time algorithm for solving the node searching spanning tree problem on unicyclic graphs.
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