GraphDisjointUnion

GraphDisjointUnion[g1, g2] gives the disjoint union of graphs g1 and g2 (vertices and edges from both, kept separate).

Examples

Disjoint union:

GraphDisjointUnion[CycleGraph[3], CycleGraph[4]]
(* Graph with 7 vertices, two separate components *)

Multiple graphs:

GraphDisjointUnion[PathGraph[{1, 2}], PathGraph[{3, 4}], PathGraph[{5, 6}]]

Please visit the official Wolfram Language Reference for more details.