Given the following graph:
Is this graph Hamiltonian or not?
The answer is no. What I tried to prove is by using the fact that: "if a vertex in the graph has degree two, then both edges that are incident with this vertex must be part of any Hamilton circuit." Following that we know, edges 11,6,4,12 must be in any circuit and the edges 17,18,19 and 9,15 must be in any circuit. Knowing that, what should I do to conclude that the graph is not Hamiltonian?