discrete maths graph, vertices edges I have connected graph has 13 edges, 2 vertex of degree 2, 2 vertex of degree
3, 1 vertex of degree 6, and all others of degree 5. But with an unknown vertices. 
I read an online article and it says that for it to be a graph, the total number of edges should be even, and e = 2v? But in this case, 13 edges cannot be formed into a graph? which means that there are 5 vertices?

You obviously missed the point in the original source. What you mean is the sum of valency of all vertices of a connected graph is even. (more precisely, the number of vertices of odd valency is even.) and obviously that Total Valency=2 $\times$ No. of Edges. These are trivial results. You can use them to solve the number of vertices.
$$2\times 13=5\times x+2\times 2+2\times 3+1\times 6\implies x=2$$. What other thing you could conclude about even is the x should be even (can you say why).
