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What is the time complexity for finding a Hamiltonian path for a graph having N vertices (using permutation)?

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What is the time complexity for finding a Hamiltonian path for a graph having N vertices (using permutation)?

(a) O(N!)

(b) O(N! * N)

(c) O(log N)

(d) O(N)

This question was addressed to me during an interview.

My question is taken from Checksum, Complexity Classes & NP Complete Problems in section Checksum, Complexity Classes & NP Complete Problems of Data Structures & Algorithms II

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Right choice is (b) O(N! * N)

To explain: For a graph having N vertices traverse the permutations in N! iterations and it traverses the permutations to see if adjacent vertices are connected or not takes N iterations (i.e.) O(N! * N).

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