翻訳と辞書 Words near each other ・ Friendship Circle ・ Friendship Collegiate Academy Public Charter School ・ Friendship contract ・ Friendship Creek ・ Friendship cup ・ Friendship Cup (tennis) ・ Friendship Dam ・ Friendship Day ・ Friendship Express ・ Friendship Festival ・ Friendship Flight '89 ・ Friendship Force International ・ Friendship Fountain ・ Friendship Free Library ・ Friendship Games ・ Friendship graph ・ Friendship Hall ・ Friendship Heights ・ Friendship Heights station ・ Friendship Highway ・ Friendship Highway (China-Nepal) ・ Friendship Hill National Historic Site ・ Friendship House ・ Friendship House (Washington, D.C.) ・ Friendship knot ・ Friendship knot loop ・ Friendship Loyalty Commitment ・ Friendship Nine ・ Friendship Oak (Long Beach, Mississippi) ・ Friendship of Salem Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Friendship graph ： ウィキペディア英語版 Friendship graph In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or ''n''-fan) ''F''''n'' is a planar undirected graph with ''2n+1'' vertices and ''3n'' edges. The friendship graph ''Fn'' can be constructed by joining ''n'' copies of the cycle graph ''C''3 with a common vertex.〔Gallian, J. A. "Dynamic Survey DS6: Graph Labeling." Electronic J. Combinatorics, DS6, 1-58, Jan. 3, 2007. ().〕 By construction, the friendship graph ''Fn'' is isomorphic to the windmill graph Wd(3,''n''). It is unit distance with girth 3, diameter 2 and radius 1. The graph ''F''2 is isomorphic to the butterfly graph. ==Friendship theorem== The friendship theorem of 〔.〕 states that the finite graphs with the property that every two vertices have exactly one neighbor in common are exactly the friendship graphs. Informally, if a group of people has the property that every pair of people has exactly one friend in common, then there must be one person who is a friend to all the others. However, for infinite graphs, there can be many different graphs with the same cardinality that have this property.〔. 〕 A combinatorial proof was given by Mertzios and Unger. Another proof was given by Craig Huneke 〔Huneke, Craig. ("The Friendship Theorem." ) The American Mathematical Monthly 109.2 (2002): 192-94. JSTOR. Mathematical Association of America. Web. 〕 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「Friendship graph」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.