# 3-regular graphs with an odd number of vertices [duplicate]

Do there exist any 3-regular graphs with an odd number of vertices? I'm starting a delve into graph theory and can prove the existence of a 3-regular graph for any even number of vertices 4 or greater, but can't find any odd ones.

## marked as duplicate by JMoravitz, Math1000, Harish Chandra Rajpoot, Claude Leibovici, Daniel W. FarlowFeb 29 '16 at 9:15

The Handshaking Lemma:$$\sum_{v\in V} \deg(v) = 2|E|$$