c) Find a Hamiltonian cycle starting at vertex A. Draw the Hamiltonian cycle on the graph and list the vertices of the cycle. A E H B F G Note: A Hamiltonian cycle is a simple cycle that traverses all vertices. A simple cycle starts at a vertex, visits other vertices once then returns to the starting vertex.
c) Find a Hamiltonian cycle starting at vertex A. Draw the Hamiltonian cycle on the graph and list the vertices of the cycle. A E H B F G Note: A Hamiltonian cycle is a simple cycle that traverses all vertices. A simple cycle starts at a vertex, visits other vertices once then returns to the starting vertex.
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Transcribed Image Text:### Hamiltonian Cycle Problem
#### Problem:
Find a Hamiltonian cycle starting at vertex \(A\). Draw the Hamiltonian cycle on the graph and list the vertices of the cycle.
#### Graph Description:
The given graph consists of 9 vertices labeled as follows:
- Top row: \(A\), \(B\), \(C\), \(D\)
- Middle row: \(E\), \(F\), \(G\)
- Bottom row: \(H\), \(I\)
Vertices \(A\) and \(B\) are connected, \(A\) to \(E\), \(E\) to \(H\), \(B\) to \(F\), \(F\) to \(I\), \(F\) to \(E\), \(B\) to \(C\), \(C\) to \(D\), \(C\) to \(G\), \(F\) to \(G\), and \(E\) to \(F\).
#### Note:
A Hamiltonian cycle is a simple cycle that traverses **all vertices**. A simple cycle starts at a vertex, visits other vertices **once** then returns to the starting vertex.
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