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:
Hamiltonian cycles = 12
- Hamiltonian Cycle | Backtracking-6
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