It depends on what traversals are given. If one of the traversal methods is Inorder then the tree can be constructed, otherwise not.

**Therefore, following combination can uniquely identify a tree.**

Inorder and Preorder.

Inorder and Postorder.

Inorder and Level-order.

And following do not.

Postorder and Preorder.

Preorder and Level-order.

Postorder and Level-order.

For example, Preorder, Level-order and Postorder traversals are same for the trees given in above diagram.

Preorder Traversal = AB

Postorder Traversal = BA

Level-Order Traversal = AB

So, even if three of them (Pre, Post and Level) are given, the tree can not be constructed.