Rooted tree

A rooted tree is a tree with a distinguished vertex called the root. Its levels consist of the vertices at a fixed graph distance from the root.

For an automorphism $g$ of a regular rooted tree and a first-level vertex $i$, the section $g_i$ is the induced automorphism of the rooted subtree at $i$, defined byAn automorphism fixing the first level is determined by the tuple of all its sections.