Question

In a 7-node directed cyclic graph, the
number of Hamiltonian cycle is to be
O 728
O 450
O 360
0 260​

Answer 1

Answer:

the answer is of this question is --- 360

Answer 2

In a 7-node directed cyclic graph, the number of Hamiltonian cycles is to be 360.

• A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once.
• A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path.
• A simple graph with n vertices in which the sum of the degrees of any two non-adjacent vertices is greater than or equal to n has a Hamiltonian cycle.
• A Hamiltonian cycle in a connected graph G is defined as a closed path that traverses every vertex of G exactly once except the starting vertex, at which the path also terminates.
• In an n-complete graph, there are (n-1)!/2 hamiltonian cycles and so the answer is 360.

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