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In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set ''X'', such that every (unordered) quadruple from ''X'' contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups. A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs. ==Examples== On the set of vertices the following collection of unordered triples is a two-graph: :123 124 135 146 156 236 245 256 345 346 This two-graph is a regular two-graph since each pair of distinct vertices appears together in exactly two triples. Given a simple graph ''G'' = (''V'',''E''), the set of triples of the vertex set ''V'' whose induced subgraph has an odd number of edges forms a two-graph on the set ''V''. Every two-graph can be represented in this way. This example is referred to as the standard construction of a two-graph from a simple graph. As a more complex example, let ''T'' be a tree with edge set ''E''. The set of all triples of ''E'' that are not contained in a path of ''T'' form a two-graph on the set ''E''.〔 cited in 〕 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「Two-graph」の詳細全文を読む スポンサード リンク
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