The graph union 
of graphs 
and 
with vertex
sets 
and 
and edge sets 
and 
is the graph with 
and 
(Skiena 1990, pp. 129-131). Vertices having
the same labels are identified, and edges common to both edge sets are not duplicated.
When 
and 
are disjoint, the graph union coincides with the graph
disjoint union.
The Wolfram Language function GraphUnion[g1, g2] computes the graph union by merging vertices and edges with shared labels.
