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In discrete mathematics, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Given a graph, the eccentricity of a vertex ''v'' is defined as the greatest distance from ''v'' to any other vertex. A ''center'' (also: ''centroid'') of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. However, has proved that for trees, there are only two possibilities: # The tree has precisely one center (centered trees). # The tree has precisely two centers (bicentered trees). In this case, the two centers are adjacent. A proof of this fact is given, for example, by Knuth.〔, p. 387 and p. 589〕 ==Notes== 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「centered tree」の詳細全文を読む スポンサード リンク
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