Vertices help

• Jun 18th 2010, 11:47 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.
• Jun 19th 2010, 12:17 AM
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.
• Jun 19th 2010, 12:26 AM
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.