Forests, Trees and Graphs

Some basic terminologies of Graphs: Trees, Forests, acorns

Recall the definition of graphs:

A graph G is a set of point VG), along with a set of edges E(G), where each element of E(G) is an unordered pair of distinct points of V(G).

Cycle

If you draw the graph and you see a closed-loop in it. The loop is called a "cycle".

Tree

A graph devoid of cycles is called a tree.

Path

A path in a graph G is an alternating sequence of points and edges, such that all the points of the path are distinct.

Every two points of a tree are joined by a unique path.

Connected Graphs

A graph is called connected if every pair of points are joined by a path. If the graph is not connected then it is made up of "subgraphs". These subgraphs are called as connected components of the graph G.

Forests

A graph for which each connected component is a tree is called a forest.

Acorn

In the forest when one of the component trees has one point but no edges joined to it. That is, it is an isolated dot. This is called an acorn.