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词汇 Symmetric graph
分类 英语词汇 英语翻译词典
释义

Symmetric graph

英语百科

Symmetric graph

The Petersen graph is a (cubic) symmetric graph.  Any pair of adjacent vertices can be mapped to another by an automorphism, since any five-vertex ring can be mapped to any other.

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1v1 and u2v2 of G, there is an automorphism

such that

In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called 1-arc-transitive or flag-transitive.

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