|
In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which all vertices are symmetric to each other, each vertex has exactly three incident edges, and these three edges are not symmetric to each other. More precisely, it is a connected vertex-transitive cubic graph whose edges are partitioned into three different orbits by the automorphism group. In these graphs, for every two vertices ''u'' and ''v'', there is exactly one graph automorphism that takes ''u'' into ''v''.〔, p. 4.〕 The name for this class of graphs was coined by R. M. Foster in a 1966 letter to H. S. M. Coxeter.〔, p. ix.〕 ==Examples== The smallest zero-symmetric graph is a nonplanar graph with 18 vertices.〔, Figure 1.1, p. 5.〕 Its LCF notation is ()9. Among planar graphs, the truncated cuboctahedral and truncated icosidodecahedral graphs are also zero-symmetric.〔, pp. 75 and 80.〕 These examples are all bipartite graphs. However, there exist larger examples of zero-symmetric graphs that are not bipartite.〔, p. 55.〕 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「Zero-symmetric graph」の詳細全文を読む スポンサード リンク
|