Does there exist a simple graph with five vertices of the following degrees?
I know that the answer is no, however I do not know how to explain this.
No, as the sum of the degrees of an undirected graph is even.
Again, I believe the answer is no however I don't know the rule to explain why.
Same as above.
What method should I use to work out whether a graph is simple, given the number of vertices and the degree sequence?