Hey guys need help with this question. "A graph has 33 edges, and every vertex has degree 7 or degree 8. How many vertices does the graph have?".

Any help would be much appreciated.

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- Jun 18th 2010, 10:47 PMjvignacioVertices help
Hey guys need help with this question. "A graph has 33 edges, and every vertex has degree 7 or degree 8. How many vertices does the graph have?".

Any help would be much appreciated. - Jun 18th 2010, 11:17 PMProve It
From the handshaking lemma

Since there are edges, that means .

That means that , where is the number of vertices with degree and is the number of vertices with degree .

By inspection, and .

So there are vertices. - Jun 18th 2010, 11:26 PMjvignacio