Challenge Level

A graph is a network of points and lines. The points are called vertices and the lines which connect them are called edges. Each edge has a vertex at each end. The branch of mathematics called graph theory studies the properties of various kinds of graphs.

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops).

Prove that every tree has exactly one more vertex than it has edges.