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Topic: The handshake lemma question?
Replies: 3   Last Post: Feb 12, 2012 1:56 PM

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Registered: 2/12/12
The handshake lemma question?
Posted: Feb 12, 2012 12:15 PM
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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.

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