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In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley) and uses a specified, usually finite, set of generators for the group. It is a central tool in combinatorial and geometric group theory. == Definition == Suppose that is a group and is a generating set. The Cayley graph is a colored directed graph constructed as follows: 〔 In his Collected Mathematical Papers 10: 403–405.〕 * Each element of is assigned a vertex: the vertex set of is identified with * Each generator of is assigned a color . * For any the vertices corresponding to the elements and are joined by a directed edge of colour Thus the edge set consists of pairs of the form with providing the color. In geometric group theory, the set is usually assumed to be finite, symmetric (i.e. ) and not containing the identity element of the group. In this case, the uncolored Cayley graph is an ordinary graph: its edges are not oriented and it does not contain loops (single-element cycles). 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「cayley graph」の詳細全文を読む スポンサード リンク
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