Rooted Tree

ROOTED TREE: A rooted tree T with the vertex set V is the tree that can be defined recursively as follows : T has a specially designated vertex v1 ∈ V, called the root of T. The subgraph of T1 consisting of the vertices V – {v} is partitionable into subgraphs.
T1, T2, ......, Tr each of which is itself a rooted tree. Each one of these r-rooted tree is called a subtree of v1.

Co tree: The cotree T* of a spanning tree T in a connected graph G is the spanning subgraph of G containing exactly those edges of G which are not in T. The edges of G which are not in T* are called its twigs.

For example :