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In the mathematical field of graph theory, an edge-transitive graph is a graph ''G'' such that, given any two edges ''e''1 and ''e''2 of ''G'', there is an automorphism of ''G'' that maps ''e''1 to ''e''2. In other words, a graph is edge-transitive if its automorphism group acts transitively upon its edges. ==Examples and properties== Edge-transitive graphs include any complete bipartite graph , and any symmetric graph, such as the vertices and edges of the cube.〔 Symmetric graphs are also vertex-transitive (if they are connected), but in general edge-transitive graphs need not be vertex-transitive. The Gray graph is an example of a graph which is edge-transitive but not vertex-transitive. All such graphs are bipartite,〔 and hence can be colored with only two colors. An edge-transitive graph that is also regular, but not vertex-transitive, is called semi-symmetric. The Gray graph again provides an example. Every edge-transitive graph that is not vertex-transitive must be bipartite and either semi-symmetric or biregular.〔.〕 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-transitive graph」の詳細全文を読む スポンサード リンク
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