graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. 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.

Notation

The disjoint union is also called the graph sum and may be represented either by a

plus sign The plus sign () and the minus sign () are mathematical symbols used to denote positive and negative functions, respectively. In addition, the symbol represents the operation of addition, which results in a sum, while the symbol represents ...

or a circled plus sign: If

G

and

H

are two graphs, then

G+H

G\oplus H

denotes their disjoint union.

Related graph classes

Certain special classes of graphs may be represented using disjoint union operations. In particular: *The forests are the disjoint unions of trees. *The cluster graphs are the disjoint unions of complete graphs. *The 2-regular graphs are the disjoint unions of cycle graphs. More generally, every graph is the disjoint union of connected graphs, its connected components. The cographs are the graphs that can be constructed from single-vertex graphs by a combination of disjoint union and complement operations.

References

{{reflist Graph operations