A tree is a connected forest. Trees and forests are examples of simple graphs . Below is a forest of four trees. Each connected component in this forest is a tree. Theorem Suppose that T is a graph with n vertices.
T is a tree.
T has n - 1 edges and no circuits. T is connected and has n - 1 edges. T is connected and each of its edges is an isthmus. Any two vertices of T are connected by exactly one simple path. T has no circuits, but the addition of any new edge creates exactly one circuit.