Tony Orlow wrote: > If we look at the children of this subroot node, they include the root, > as well as the subroot itself. That's an interesting...twist, or loop, as one might > call it. > > So, in conclusion, the "complete" binary tree includes not only a root > node, but a subroot node, which is its own parent, akin to the missing > fifth of a point on the top of the pyramid.
The root node of a tree has no parent (by definition), so if your "root" node has a parent, it cannot be the root node of the tree.
This thing you're describing is not a tree (because a tree does not contain cycles), so you really should find a different name for it. T-tree? Rootless tree? Rootful tree? Tooth tree?
(It appears you may be confusing abstract trees with heirarchical file systems, which share many of the properties of trees but which are not true mathematical trees, but graphs.)