Option B: FECBAD is the Hamilton path
Explanation:
Given that ABCDEF is a graph with vertices A,B,C,D,E and F
We need to determine the Hamilton path.
Since, we know that a Hamilton path is a path that touches every vertex in a graph exactly once.
Option A: EFADECBA
The path touches the vertices E and A twice.
Hence, the path EFADECBA is not a Hamilton path.
Therefore, Option A is not the correct answer.
Option B: FECBAD
The path touches every vertex in the graph exactly once.
Hence, the path FECBAD is a Hamilton path.
Therefore, Option B is the correct answer.
Option C: ADEFBD
The path touches the vertex A twice because when the path travels from F to B the only way to travel through A.
Hence, the path ADEFBD is not a Hamilton path.
Therefore, Option C is not the correct answer.
Option D: ADECBAFE
The path touches the vertices E and A twice.
Hence, the path ADECBAFE is not a Hamilton path.
Therefore, Option D is not the correct answer.
