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).
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).