Given an undirected complete graph of N vertices where N > 2. The task is to find the number of different Hamiltonian cycle of the graph.
Complete Graph: A graph is said to be complete if each possible vertices is connected through an Edge.
Hamiltonian Cycle: It is a closed walk such that each vertex is visited at most once except the initial vertex. and it is not necessary to visit all the edges.
Input : N = 6 Output : Hamiltonian cycles = 60 Input : N = 4 Output : Hamiltonian cycles = 3
Let us take the example of N = 4 complete undirected graph, The 3 different hamiltonian cycle is as shown below:
Below is the implementation of the above approach:
// Java program for implementation
// of the above program
// Function that calculates
// number of Hamiltonian cycle
static int Cycles(int N)
int fact = 1, result = 0;
result = N – 1;
// Calculating factorial
int i = result;
while (i > 0)
fact = fact * i;
return fact / 2;
// Driver code
public static void main(String args)
int N = 5;
int Number = Cycles(N);
System.out.println(“Hamiltonian cycles = ” +
// This code is contributed
// by Code_Mech.
Hamiltonian cycles = 12
- Hamiltonian Cycle | Backtracking-6
- Total number of Spanning trees in a Cycle Graph
- Number of single cycle components in an undirected graph
- Proof that Hamiltonian Path is NP-Complete
- Degree of a Cycle Graph
- C++ Program for Cycle Sort
- Coloring a Cycle Graph
- Detect cycle in an undirected graph using BFS
- Detect cycle in an undirected graph
- Detect Cycle in a Directed Graph
- Detect Cycle in a Directed Graph using BFS
- Check if a graphs has a cycle of odd length
- Detect Cycle in a directed graph using colors
- Detecting negative cycle using Floyd Warshall
- Check if there is a cycle with odd weight sum in an undirected graph
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.