I got something interesting on this Problem.Generating X values it shows ϕ(N) for N.But i can't evaluate why this picture follows phi function.Can anyone explain me theory behind it? How co-primes are related with skipping X on this problem?

I am trying with Articulation point + Kruskal.... Imperial roads That's why my code becomes so large and i can't fix bug. Is there any other approach? Or give me corner case for my code