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## 'Tree Graphs' printed from http://nrich.maths.org/

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.