Page "Cograph" Paragraph 23

An equivalent way of describing the cograph formed from a cotree is that two vertices are connected by an edge if and only if the lowest common ancestor of the corresponding leaves is labeled by 1.

Conversely, every cograph can be represented in this way by a cotree.

If we require the labels on any root-leaf path of this tree to alternate between 0 and 1, this representation is unique.