For A[0] = v₁, A[1] = v₁, A[2] = v₁, bubble sort will make the comparisons indicated by :.

Bubble sort swaps values if they are out of order. This determines the next comparison.

Assumming no duplicates, there are only 2 possible results of each comparison. So we get a binary tree.

The red edges are never true, so some comparisons are not necessary.

However, we must have 6 leaf nodes corresponding to the 6 possible orderings of {v₁, v₂, v₃}