longest path in geraph

Your question
1) is not in line with the CP guideleines[^]: "I want..." is at the edge of being impolite
2) lacks crucial details like graph kind, if performance/memory/... matters, if you ask for papers or code, ...?
3) does not give background of what you did try yourself (asking Goolge is the minimum one can expect nowadays)...

Nonetheless, I assume now you have a DAG - Directed Acyclic Graph[^]:
- Google: DAG longest path[^]
- http://en.wikipedia.org/wiki/Longest_path_problem[^]
- ...

Cheers
Andi