Suppose we have two full binary trees, illustrated in the image below:
- $T_1$ is the tree formed by the solid nodes ($a, b, c$).
- $T_2$ is the tree considering both solid and dashed nodes ($a,b,c,d,e$).
Is there a name for the operation that transforms $T_1$ into $T_2$? We're taking a leaf node ($c$) and adding $m$ children to it.
What about the inverse operation transforming $T_2$ into $T_1$? Is there a name used for it?
I found many different references for definitions on $m$-ary trees, but none mentioned operations on trees.