Tarjan Strongly Connected Components Question
v.lowlink = min(v.lowlink, v'.index) in line 16 is indeed correct. For a full proof you can consult Tarjan's original paper which can also be found here.


  Robert Tarjan: Depth-first search and
  linear graph algorithms. In: SIAM
  Journal on Computing. Vol. 1 (1972),
  No. 2, P. 146-160.


Completely unrelated to the question, there is an amusing 1983 retrospective by Bob Tarjan here on the paper cited above.