depth first search - DFS and BFS trees related to undirected connected simple graph -

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In view of an unrestricted linked simple graph, TD should be a DFS tree and be a BFS tree of TBB Peak

If TB and TD are similar then G is an esical graph, is it always true?

I worked on the following example:

TD and TB: 

  (A, B) (A, C (B, D) (B, E) (C, F) (C, G)

and then the graph can be: 

  (A, B) (A , C) (B, D) (B, E) (C, F) (C, G) (C, A)

Am I thinking the right direction? Because this problem The answer given for is true which should be wrong according to me.

Please help


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