Euler's polyhedron theoremEulersPolyhedronTheorem2002-02-21 18:33:232006-10-04 18:04:14Theoremgraphvertexedgefacevertices% this is the default PlanetMath preamble. as your knowledge
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% define commands here\newtheorem{thm}{Theorem}
\begin{thm}[]
If a connected plane graph has $n$ vertices, $m$ edges, and $f$ faces, then
$$n - m + f = 2.$$
\end{thm}