Option B: FECBAD represents the Hamilton path
Step-by-step explanation:
The vertices in the given graph are A,B,C,D,E and F
We need to determine the Hamilton path of the given graph.
By definition, we know that a Hamilton path touches each and every vertex in a graph exactly once.
Hence, we need to connect the vertices in such a way that the graph touches each and every vertex exactly once.
Option A: EFADECBA
From this description, we can see that the path starts from the vertex E and connects all the vertices but some of the vertices are repeated twice.
Hence, the path EFADECBA is not a Hamilton path.
Therefore, Option A is not the correct answer.
Option B: FECBAD
From this description, we can see that the path starts from the vertex F and connects all the vertices exactly once.
Hence, the path FECBAD is the Hamilton path.
Therefore, Option B is the correct answer.
Option C: ADEFBC
From this description, we can see that the path starts from the vertex A and connects all the vertices but the path from F to B has to touch the vertex A. Thus, the vertices are repeated twice.
Hence, the path ADEFBC is not a Hamilton path.
Therefore, Option C is not the correct answer.
Option D: ADECBAFE
From this description, we can see that the path starts from the vertex A and connects all the vertices but some of the vertices are repeated twice.
Hence, the path ADECBAFE is not a Hamilton path.
Therefore, Option D is not the correct answer.