Vertices help

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June 18th 2010, 10:47 PM
jvignacio

Vertices 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.
June 18th 2010, 11:17 PM
Prove It

From the handshaking lemma

$\sum{\textrm{deg}\,(v)} = 2|E|$

Since there are $33$ edges, that means $\sum{\textrm{deg}\,(v)} = 66$ .

That means that $7m + 8n = 66$ , where $m$ is the number of vertices with degree $7$ and $n$ is the number of vertices with degree $8$ .

By inspection, $m = 6$ and $n = 3$ .

So there are $9$ vertices.
June 18th 2010, 11:26 PM
jvignacio

Quote:

Originally Posted by Prove It

From the handshaking lemma

$\sum{\textrm{deg}\,(v)} = 2|E|$

Since there are $33$ edges, that means $\sum{\textrm{deg}\,(v)} = 66$ .

That means that $7m + 8n = 66$ , where $m$ is the number of vertices with degree $7$ and $n$ is the number of vertices with degree $8$ .

By inspection, $m = 6$ and $n = 3$ .

So there are $9$ vertices.

Thank you for your reply! Nice and clear.

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