**Valence and Face Vectors: An Example**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

If G is a plane graph, embedded in the plane (no accidental crossings) then G has both a "valence vector" and "face vector."

v_{i} = the number vertices of the graph of valence i

p_{k} = the number of faces of the graph with k sides.

v_{2} = 4; v_{3} = 7; v_{4} = 1; v_{5} = 3

p_{3} = 6; p_{4} = 2; p_{6} = 1; p_{7} = 1; p_{9} = 1