Question

Draw three different B-trees of degree 3 with height 4.

Short answer

Therefore, the draw of three different B-trees of degree 3 with height 4 is shown below.

Step-by-step solution

General form

Definition of tree: A tree isa connected undirected graph with no simple circuits.

Definition of Circuit:It is a path that begins and ends in the same vertex.

B-tree of degree k(Definition):It is a rooted tree such that all its leaves are at the same level, its root has at least two and at most k children unless it is a leaf, and every internal vertex other than the root has at least \(\left\lceil {\frac{{\bf{k}}}{{\bf{2}}}} \right\rceil \), but no more than k, children.Computer files can be accessed efficiently when B-trees are used to represent them.

Proof of the given statement

Given that, a B-tree of degree 3 with height 4.

Possibilities of B-tree graph:

1. All leaves are at level 4.
2. At least 2 and at most 3 children at every internal vertex.
3. The longest path in the rooted tree has to be of length 4.

The graph of the B-trees is shown below.

Since, the graphs are represented possibilities of B-trees.