Graph Intersection


Let S be a set and F={S_1,...,S_p} a nonempty family of distinct nonempty subsets of S whose union is  union _(i=1)^pS_i=S. The intersection graph of F is denoted Omega(F) and defined by V(Omega(F))=F, with S_i and S_j adjacent whenever i!=j and S_i intersection S_j!=emptyset. Then a graph G is an intersection graph on S if there exists a family F of subsets for which G and Omega(F) are isomorphic graphs (Harary 1994, p. 19). Graph intersections can be computed in the Wolfram Language using GraphIntersection[g, h].

See also

Graph Union, Intersection Number

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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.

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