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
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