# What order B-tree is this?

I am studying B-trees and reading Introduction to Algorithms by Cormen et al.

Unfortunately, they have this diagram Figure 18.1 and they do not list the order of the tree. I understand that for a B-tree of order $$m$$, the tree has 5 properties:

1. Every node has at most $$m$$ children.
2. Every internal node except the root has at least $$\left\lceil \frac{m}{2}\right \rceil$$ children.
3. Every non-leaf node has at least two children.
4. All leaves appear on the same level and carry no information.
5. A non-leaf node with $$k$$ children contains $$k−1$$ keys.

Based on this however, I wasn't sure if you could just tell the order of a given tree. To me, it seems this looks like it could be order 4,5, or 6. By the $$\left\lceil \frac{m}{2}\right \rceil$$ criteria, 6 would be the most since 6/2 = 3 and therefore anything larger would automatically mean that this criteria wouldn't be satisfied for the node with keys D,H.

Is the order of a B-tree unique? If so, what is the order of this B-tree?

You have given the answer. A B-tree of order $$4$$ can also be a B-tree of order $$5$$ or $$6$$. So, "the order" of a B-tree may not be unique.
So, according to Knuth, the order of the B-tree in the question is $$4$$.