Definition:Euler Characteristic of Finite Graph

Graphs
The Euler Characteristic of a graph $$X \ $$ is $$\chi(X) = v-e+f \ $$, where $$v \ $$ is the number of vertices, $$e \ $$ the number of edges, and $$f \ $$ the number of "faces."

Faces are regions of a plane completely bounded by edges, or completely exterior to the graph.

Euler Polyhedron Formula
The Euler Polyhedron Formula states that for any graph which can be drawn on a sphere or plane, $$\chi = 2 \ $$.

Generalized Formula
The unproved statements on this page are just resting here until they can be proved on pages of their own.