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All the places where I have read the Ham-Cycle problem, the graph used is directed.

 

Is the problem of finding Ham-Cycle on an undirected graph also NP-Complete or not?

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Got it. Both problems are stated differently, but both are NP-Complete.

 

 The mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete.

 

Source: https://en.wikipedia.org/wiki/Hamiltonian_path_problem

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