Prove that if G contains an odd vertex then every vertex of G is odd Let G be a graph with degree of each vertex either $m$ or $n$, where there are $m$ vertices of degree $m$ and $n$ vertices of degree $n$. Prove that if G contains an odd vertex then every vertex of G is odd.
how do I go about this? What does it imply if G contains an odd vertex? Also, how am I to use the first line of the given problem? Please help.

A very useful elementary result in graph theory is the degree sum formula:
$$\sum_{v\in V}\deg(v) = 2\lvert E \rvert$$
for a graph $G=(V,E)$.
In particular the sum of the degrees of the vertices is even.
Now what can you say if some vertex has odd degree?
