Disjoint union of graphs

It is analogous to the disjoint union of sets, and is constructed by making the vertex set of the result be the disjoint union of the vertex sets of the given graphs, and by making the edge set of the result be the disjoint union of the edge sets of the given graphs.

Any disjoint union of two or more nonempty graphs is necessarily disconnected.

The disjoint union is also called the graph sum, and may be represented either by a plus sign or a circled plus sign: If

[1] Certain special classes of graphs may be represented using disjoint union operations.

The cographs are the graphs that can be constructed from single-vertex graphs by a combination of disjoint union and complement operations.