I am trying to brush up my graph theory skills. I have not done any in over 4 years and i am rusty...If someone could help me out with this simple proof i would appreciate it.
Prove that for any graph $G$ of order at least 2, the degree sequence has at least one pair of repeated entries.
So the degree sequence if a list of the degrees of each vertex (usually written in descending order).
I know that the sum of the degrees of the vertices of a graph is equal to $2|E|$ and that the number of vertices of odd degree is even.
If someone could help me out and point me in the right direction i would appreciate it.