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Euler's polyhedron theorem (Theorem)
Theorem 1   If a connected plane graph has $n$ vertices, $m$ edges, and $f$ faces, then $$n - m + f = 2.$$



"Euler's polyhedron theorem" is owned by Mathprof. [ full author list (2) | owner history (1) ]
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See Also: graph, graph theory, Poincaré formula, polytope

Other names:  Euler's formula
Keywords:  graph, vertex, edge, face, vertices

Attachments:
proof of Euler's polyhedron theorem (Proof) by mps
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Cross-references: faces, edges, vertices, plane graph, connected
There are 10 references to this entry.

This is version 3 of Euler's polyhedron theorem, born on 2002-02-21, modified 2006-10-04.
Object id is 2433, canonical name is EulersPolyhedronTheorem.
Accessed 10801 times total.

Classification:
AMS MSC: 05C99 (Combinatorics :: Graph theory :: Miscellaneous)
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