Hamiltonian path and it's algorithm

HAMILTONIAN PATH

• Hamiltonian Path is a path in a directed or undirected graph that visits each vertex exactly once. The problem to check whether a graph (directed or undirected) contains a Hamiltonian Path is NP-complete, so is the problem of finding all the Hamiltonian Paths in a graph. 
• Hamiltonian Path in a graph having N vertices is nothing but a permutation of the vertices of the graph [v1, v2, v3, ......vN-1, vN] , such that there is an edge between vi and vi+1 where 1 ≤ i ≤ N-1. So it can be checked for all permutations of the vertices whether any of them represents a Hamiltonian Path or not.
•  In 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.

• The Hamiltonian cycle problem is a special case of the travelling salesman problem, obtained by setting the distance between two cities to one if they are adjacent and two otherwise, and verifying that the total distance travelled is equal to n (if so, the route is a Hamiltonian circuit; if there is no Hamiltonian circuit then the shortest route will be longer).