B-Plus-Tree | B Tree | Dataset library

Both methods are correct.

The difference that you highlight is not so much in deleting/not-deleting internal keys, but in updating/not-updating them.

Obviously, when you delete a value (i.e. a key in a leaf node), the b-plus-tree property is not violated: all child values are still within the range dictated by the parent information. You can never break this range-rule by merely removing a value from a leaf. This rule is also still valid when you update the internal key(s) in the path to that leaf (according to method 1), which is only necessary when the deleted value was the left-most one in its leaf.

Note that the two methods may produce quite different trees after a long sequence of the same operations (insert, delete).

But on average the second method will have slightly less work to do. This difference is not significant though.