No. of vertex in a undirected graph

Question

I think the answer to this problem is 9 whereas given answer is 8. My approach was using sum of degree theorm,

6(no. of vertex with degree 3) * 3 + x(no.of vertices which we need to find out) *( degree less than 3)  = 2*|E| {|E| = 12 given}

i.e 18 + x*(deg less than 3) = 24

so as degree of x is less than 3 so at max it can be 2 and to make no.of vertices min. it should be 2

therefor x*2 = 6 i.e x = 3

and total vertices = 9 whereas ans.given is 8. please provide a clear explanation.

Comments

yes 9 should be correct.

---

that's what i think but answer given is 8. i don't know how!

---

Actually in answer they are using 3 max degree for rest of vertices
But i think your approach is  right

Answer 1

Minimum number of vertices G can have is 9 and graph can either be connected or disconnected having 2 component

If disconnected:

First component having 6 vertices and 9 edges and

Second component having 3 vertices complete graph.

If connected