$k$-regular graph Let $G$ be a $k$-regular graph with $m$ edges and $k$ odd. Prove that $k\mid m$.
We can see this statement is true by example, but how can we prove it?

HINT: Use the handshaking lemma: if $V$ is the vertex set of $G$, then $\sum_{v\in V}\deg v=2m$. Say there are $n$ vertices; what is $\sum_{v\in V}\deg v$ in terms of $n$ and $k$?
