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joe
Posts:
3
Registered:
2/12/12


The handshake lemma question?
Posted:
Feb 12, 2012 12:15 PM


Hi, everyone I'm having a bit of trouble with this problem. I don't understand it at all. Any help will be appreciated
Consider a planar graph with v vertices, e edges, and f face.
A)The degree of a vertex is de?ned as the number of edges touching it. Let?s de?ne in an analogous way the degree of a face to be the number of edges encountered when we complete a walk around its boundary. What happens if we add up the degrees of all faces (note: this includes the outer face too).
B)From part (a), conclude a relation between the sum of degrees of vertices and the sum of degrees of faces.



