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.
A unique binary tree cannot always be constructed using:
- 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 all three traversals (Preorder, Postorder and Level-order) are given, the tree cannot be uniquely constructed.