3-regular graphs with an odd number of vertices

Question

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.

Answer 1

The following is useful:

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

Corrollary: The number of vertices of odd degree in a graph must be even.

Corrollary 2: No graph exists with an odd number of odd degree vertices.

Answer 2

An odd number of odd vertices is impossible in any graph by the Handshake Lemma.