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?

Let $Q$ be the number of vertices of degree $5$. Then the sum of the degrees of the vertices is $(2)(2)+(2)(3)+(1)(6)+(5)(Q)=16+5Q$. On the other hand, the sum of the degrees equals twice the numbeer of edges, which is twice $13$, which is $26$. Set these equal, solve for $Q$, and you'll have the number of vertices of degree $5$, and then you'll have the number of vertices, total. 
