The union 
of graphs 
and 
with disjoint point sets 
and 
and edge sets 
and 
is the graph with 
and 
(Harary 1994, p. 21; Gross and Yellen 2006,
p. 85). The graph (disjoint) union is denoted 
by Knuth (2024, p. 23).
When the vertices and edges of 
and 
are considered distinct regardless of their labels, the
operation is sometimes known as the graph disjoint union in order to distinguish
it from the graph union operation that merges vertices and edges with shared labels
when taking the unions of edges and vertices in 
and 
.
The Wolfram Language function GraphUnion[g1, g2] takes the graph union by merging labeled vertices and edges, while GraphDisjointUnion[g1, g2, ...] treats vertices and edges in the components as distinct regardless of their labels.
The graph disjoint union of 
copies of a graph 
is commonly denoted 
(Harary 1990, p. 21).
