In graph theory, a branch of mathematics, an undirected graph is called an **asymmetric graph** if it has no nontrivial symmetries.

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 onto itself 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.

Read more about Asymmetric Graph: Examples, Properties, Random Graphs, Trees

### Other articles related to "asymmetric graph, asymmetric, graphs":

**Asymmetric Graph**- Trees

... The smallest

**asymmetric**tree has seven vertices it consists of three paths of lengths 1, 2, and 3, linked at a common endpoint ... In contrast to the situation for

**graphs**, almost all trees are symmetric ...

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