Asymmetric graph

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.

[5] According to a strengthened version of Frucht's theorem, there are infinitely many asymmetric cubic graphs.

[1] Any n-vertex asymmetric graph can be made symmetric by adding and removing a total of at most n/2 + o(n) edges.

In contrast, again informally, "almost all infinite graphs have nontrivial symmetries."

[1] The smallest asymmetric tree has seven vertices: it consists of three paths of lengths 1, 2, and 3, linked at a common endpoint.