Asymmetric graph
Undirected graph with no non-trivial symmetries / From Wikipedia, the free encyclopedia
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In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/3/36/Frucht_graph.dot.svg/220px-Frucht_graph.dot.svg.png)
Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and v are adjacent if and only if p(u) and p(v) are adjacent. The identity mapping of a graph is always an automorphism, and is called the trivial automorphism of the graph. An asymmetric graph is a graph for which there are no other automorphisms.
Note that the term "asymmetric graph" is not a negation of the term "symmetric graph," as the latter refers to a stronger condition than possessing nontrivial symmetries.