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In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations: #Addition of a single isolated vertex to the graph. #Addition of a single dominating vertex to the graph, i.e. a single vertex that is connected to all other vertices. For example, the graph of the figure is a threshold graph. It can be constructed by beginning with a single-vertex graph (vertex 1), and then adding black vertices as isolated vertices and red vertices as dominating vertices, in the order in which they are numbered. Threshold graphs were first introduced by . A chapter on threshold graphs appears in , and the book is devoted to them. == Alternative definitions == An equivalent definition is the following: a graph is a threshold graph if there are a real number and for each vertex a real vertex weight such that for any two vertices , is an edge if and only if . Another equivalent definition is this: a graph is a threshold graph if there are a real number and for each vertex a real vertex weight such that for any vertex set , is independent if and only if The name "threshold graph" comes from these definitions: ''S'' is the "threshold" for the property of being an edge, or equivalently ''T'' is the threshold for being independent. 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「threshold graph」の詳細全文を読む スポンサード リンク
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