Question

Let G be a graph with vertex set V = { v1, v2, v3, v4, v5}.

Is it possible for the degrees of the vertices to be 3, 6, 2, 1, 5, respectively? Why or why not?

Answer 1

See your next post to find out how to calculate the number of edges.
Hence deduce if such a graph can exist or not.

Answer 2

MathMate: Is this correct for the following problem?

3 + 6 + 2 + 1 + 5

2E = 17

E = 8.5

If your allowed to have a decimal as an answer, then to come up with the answer for the amount of edges then yes it is possible for the degrees of the vertices to be 3, 6, 2, 1, 5. If your not allowed to have a decimal as an answer for the amount of edges, then no its not possible for the degrees of the vertices to be 3, 6, 2, 1, 5.