gives the subtree at a given key
gives the subtree at a given key
gives the subtree at a given path
gives the subtree at a given path
returns 'true' if there is a subtree at the given key
returns 'true' if there is a subtree at the given key
returns 'true' if there is a subtree at the given path
returns 'true' if there is a subtree at the given path
returns 'true' if there is a subtree at the given path
returns 'true' if there is a subtree at the given path
a null-graph (no verticies/K0)
create a tree with a single vertex (a singleton graph)
Add an key to the start of each existing key, effectively creating a new tree with the existing tree as a single subtree
gives the subtree at a given key