Let
be a set and
a nonempty family of distinct nonempty subsets of whose union is . The intersection graph of is denoted and defined by , with and adjacent whenever and . Then a graph is an intersection graph on if there exists a family of subsets for which and are isomorphic graphs
(Harary 1994, p. 19). Graph intersections can be computed in the Wolfram
Language using `GraphIntersection`[*g*,
*h*].

# Graph Intersection

## See also

Graph Union, Intersection Number## Explore with Wolfram|Alpha

## References

Harary, F.*Graph Theory.*Reading, MA: Addison-Wesley, 1994.Skiena, S. "Unions and Intersections." §4.1.1 in

*Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica.*Reading, MA: Addison-Wesley, pp. 129-131, 1990.

## Referenced on Wolfram|Alpha

Graph Intersection## Cite this as:

Weisstein, Eric W. "Graph Intersection."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphIntersection.html