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The graph union is defined as:
G1(V1,E1) U G2(V2,G2) = GU(V1 U V2, E1 U E2)

Transpose of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G. That is, if G contains an edge (u,v) then the converse/transpose/reverse of G contains an edge (v,u) and vice versa.

The complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G

graph intersection: G1 ∩ G2 = (V1 ∩ V2, E1 ∩ E2)