# Proof of Simple graph using vertex degrees

I think that this graph exists because the Handshaking Lemma says that the sum of the vertex degrees must be an even number. The sum of the vertices is, $1 + 2+3+4+4 = 14$ . I know that a simple graph is a graph with no loops or multiple edges. I am confused on why this graph does not exist.

• If a graph exists, it's degree sequence follows the handshaking lemma. That doesn't necessarily mean that if a degree sequence follows the handshaking lemma, the graph must exist. Apr 21, 2017 at 22:53