A Hamiltonian Cycle is a tour that visits each vertex in a graph exactly once.

Input: An unweighted graph G.
Output: Does there exist a simple tour that visits each vertex in G without
    repetition?
 

This can be reduced into the Traveling salesperson problem. The two problems are very similar: each asks for a tour that visits each vertex once. The primary difference is that the TSP is on a weighted graph.  Here is the reduction:

Hamiltonian Cycle(G= (V,E))
    Construct a complete weighted graph G' = (V',E') where V' = V
    n = |V|
    for i = 1 to n do
        for j = 1 to n do, if (i,j) exists in E then w(i,j) = 1 else w(i,j) = 2
    Return answer to TSP(G',n)
 

TSP
Input :  A weighted graph G and a value n
Output: Does a simple tour exist in G so every vertex is visited exactly once and
    the sum of the edges traveled is equal to n.

In order to get a cost n in the TSP problem, then the weight each edge in G' traveled must equal 1. This mean that the edge is in G and a Hamiltonian Cycle exists.
 
 

The answer to the the two problems will be identical.
 
 

Thank You....
 

Yes, I still haven't turned in my programming project.......