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? Collections: Mathematics