I'm currently revisiting some graph theory and have ran into the following graph.
I am to prove if it is Hamiltonian or not.
To my knowledge there is no definite or "good" theorems to determine if a graph is Hamiltonian (or not, i.e. Ore's, Dirac's) nor do we have any time/space efficient algorithms for checking larger graphs.
I have checked algorithmically that this connected graph of two Petersen subgraphs is not Hamiltonian though I don't know how to prove it mathematically.
Can anyone suggest a good angle of approach or a possible solution to mathematically proving that the graph below is not Hamiltonian?
Is it plausible to prove that it is non-Hamiltonian by the fact Petersen graphs are not Hamiltonian?
