Q: Can a graph of order 10 have one vertex of degree 8, four vertices of degree 7, four of degree 3, and one of degree 2?
That is, can the graph 8,7,7,7,7,3,3,3,3,2 exist?
I am told the answer is no. However, for multigraphs yes this is possible. I don't know why. I have tried using the Handshake Theorem, but that doesn't tell me much.
Does anybody know which theorem proves that the graph above cannot exist unless it is a multigraph? What is the reason why it cannot exist?