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