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In graph theory, an edge-graceful graph labeling is a type of graph labeling. This is a labeling for simple graphs in which no two distinct edges connect the same two distinct vertices, no edge connects a vertex to itself, and the graph is connected. Edge-graceful labelings were first introduced by S. Lo in his seminal paper.〔Lo (1985)〕 == Definition == Given a graph ''G'', we denote the set of edges by ''E''(''G'') and the vertices by ''V''(''G''). Let q be the cardinality of ''E''(''G'') and ''p'' be that of ''V''(''G''). Once a labeling of the edges is given, a vertex ''u'' of the graph is labeled by the sum of the labels of the edges incident to it, modulo ''p''. Or, in symbols, the induced labeling on the vertex ''u'' is given by : where ''V''(''u'') is the label for the vertex and ''E''(''e'') is the assigned value of an edge incident to ''u''. The problem is to find a labeling for the edges such that all the labels from 1 to ''q'' are used once and the induced labels on the vertices run from 0 to ''p'' − 1. In other words, the resulting set for labels of the edges should be and for the vertices. A graph ''G'' is said to be edge-graceful if it admits an edge-graceful labeling. 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「Edge-graceful labeling」の詳細全文を読む スポンサード リンク
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