In a group of 4 people, is it possible for each person to have exactly 3 friends? In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?
My solution
n Let G be a graph with 4 vertices, one vertex representing each person in the group.
Join two vertices u and v by an edge if and only if u and v are friends. Then the degree of
each vertex equals the number of friends that the corresponding person has. If each person
has exactly 3 friends, then each vertex has degree 3. Therefore, the total degree would be
3 · 4 = 12. This is an even number.
$n\equiv 0\pmod{2}$ and $n>3$
So It is possible.
Is this correct?

Easy solution. They're all friends with each other but not themselves. That's all, no graphs.
