Originally Posted by

**geometrywiz** If anyone could give any suggestions or help me solve this it would be greatly appreciated!

Problem Use induction to prove the following theorem. For the purposes of this question, a graph is a finite set of points in the plane, some of which are connected by straight line segments, none of which intersect. A

graph is connected if you can get from any point of the graph to any other by going on the line segments.

Theorem. Suppose G is a connected graph. Then

vG + rG = eG + 2 (1)

where

vG is the number of points.

rG is the number of regions (counting the innite outside area as one region).

eG is the number of line segments.