A Study of Node Search Spanning Tree Problem On Unicyclic Graph

• Main Authors: Shang-Yi Yang, 楊上逸
• Other Authors: Sheng-Lung Peng
• Format: Others
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/2hyew2

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.