The graph intersection 
of graphs 
and 
is commonly defined as the graph
with vertex set 
and edge set 
(Skiena 1990, pp. 129-131).
The Wolfram Language function GraphIntersection[g1,
g2] instead retains the union of the vertex sets,
returning the graph with vertex set 
and edge set 
. Thus vertices not incident to an edge
common to both graphs remain as isolated vertices.
