Problem solving by using Graph Theory

Question

In a group of 9 people, is it possible for every one to know exactly 3 other people in the group?

I just learnt a theorem that in any graph G, the number of odd vertices in G is even.

Does it related to the question stated?

Answer 1

Represent each person by a vertex and if two people know each other, connect them with an edge. If everyone knows exactly $3$ other people in the group, every vertex has degree $3$. Now, you can use your theorem to see why it is impossible.