文章摘要
引用本文:侯 远.连通图的度距离和Wiener指数[J].福州大学学报(自然科学版),2014,42(1):12~17
连通图的度距离和Wiener指数
Wiener index and degree distance of connected graphs
  
DOI:10.7631/issn.1000-2243.2014.01.0012
中文关键词: 连通图  Wiener指数  度距离  图变换
英文关键词: connected graph  Wiener index  degree distance  graph transformations
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作者单位
侯 远 福州大学至诚学院福建 福州 350002 
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中文摘要:
      P+(n)表示圈没有公共边的n阶连通图的集合,P+(n,m)表示P+(n)中具有m(m≥1)个极小圈的连通图集合. 证明了当n≥6时,P+(n,m)中具有最小度距离的图是花F(n,m),它是m个具有一个公共顶点的三角形并在公共顶点粘上n- 1-2m条悬挂边的图;同时证明P+(n)中具有最小度距离的图是F(n,1),它是一个三角形并在一个顶点上粘n-3条悬挂边的图.
英文摘要:
      Let P+(n) be the set of conneted graphs whose each pair of minimal cycles have no common edges and P+(n,m) be the set of conneted graphs with m(m≥1) minimal cycles in P+(n). For n≥6,we proved that the extremal graph with minimal degree distance in P+(n,m) is a follower F(n,m) which is m triangles sharing a common vertex on which n-1-2m pendent edges attached. Furthermore,we proved that the extremal graph with minimal degree distance in P+(n) is the graph F(n,1) which consists of a triangle and n-3 pendent edges attached to one vertex of it.
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