한 사이클 내에서 최대 가중치 간선을 제거하기 위한 최소 신장트리 알고리즘

Abstract

Abstract This paper suggests a method that obtains the minimum spanning tree (MST) far more easily and rapidly than the present ones. The suggested algorithm, firstly, simplifies a graph by means of reducing the number of edges of the graph. To achieve this, it applies a method of eliminating the maximum weight edge if the valency of vertices of the graph is equal to or more than 3. As a result of this step, we can obtain the reduced edge population. Next, it applies a method in which the maximum weight edge is eliminated within the cycle. On applying the suggested population minimizing and maximum weight edge deletion algorithms to 9 various graphs, as many as the number of cycles of the graph is executed and MST is easily obtained. It turns out to lessen 66% of the number of cycles and obtain the MST in at least 2 and at most 8 cycles by only deleting the maximum weight edges. Key Words : Minimum Spanning Tree, Valency, Cycle, Maximum Weight Edge Ⅰ. 서 론 그래프  는 정점들 (Vertices, )과 간선들(Edges, )로 구성되어 있으며, 일반적으로 그래프란 모든 정점들을 연결하는 간선들이 무방향성 (Undirected)을 갖고 있는 무방향 그래프 (Undirected Graph)를 의미