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Suppose we have a simple connected planar graph. Let V be the number of vertices and E the number of edges.
 

Summary: Theorem
Suppose we have a simple connected planar graph.
Let V be the number of vertices and E the number of edges.
Then 3V - 6 E.
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?
Let's pretend our graph is the floor plan of a house.
So each "room," counting the outside, is a face.
Suppose you have to paint the walls (inside and out).
How many walls will you have to paint?

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics