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Sat 22 Oct, 2005 09:33 pm
(i).
Let G be a simple connected cubic plane graph, and let phi_k be the number of
k-sided faces. By counting the number of vertices and edges of G, prove that:
3*phi_3 + 2*phi_4 + phi_5 - phi_7 - 2*phi_8 - . . . = 12
(ii).
Deduce that G has at least one face bounded by at most five edges.
If G is a simple connected planar cubic graph then:
| f | = 2 + | v |/2
I don't get the counting part?
Why do we need to count the number of nodes and edges to come up with the number of k-sided faces' sum?
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