3. If and are cographs, then so is their graph
union

(Brandstadt et al. 1999).

Note that cographs have been discovered independently many times since the 1970s, so no particular definition or terminology should be considered standard. Brandstadt
et al. (1999) contains references for many of the independent discoveries/definitions/characterizations
of cographs.

A graph is a cograph if any of the following
equivalent conditions holds:

1. can be constructed from isolated vertices
by disjoint union and graph join operations.

2. is the disjoint union of distance-hereditary
graphs with diameter at most 2.

The numbers of cographs on ,
2, ... nodes are 1, 2, 4, 10, 24, 66, 180, 522, 1532, ... (OEIS A000084).
Brandstadt et al. (1999, definition 1.5) note that a graph is a cograph if
its modular decomposition tree contains only parallel and series nodes. More specifically
and explicitly, the counts of cographs on nodes are the same as the counts of series-parallel
networks with
unlabeled edges, as noted by Weisstein (2003ab) and proved by Sloane. The first cographs
on to 5 nodes are illustrated above.
For , the number of cographs is always
even.