In the above graph, the blue line shows a cycle of length $84$, the remaining edges are higlihtged in red. In total, the graph has $100$ vertices and $143$ edges.
- Is this the longest cycle in this graph ?
The graph has no hamilton cycle because deleting the vertices $8$ and $20$ splits the graph into $3$ components. Deleting the vertices $1,5,8,13,20,22,25,37$ splits the graph into $10$ components, so it contains not even a hamiltonian path.
- How can I get the length of the longest cycle ?