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.

v₂ = 4; v₃ = 7; v₄ = 1; v₅ = 3

p₃ = 6; p₄ = 2; p₆ = 1; p₇ = 1; p₉ = 1