intersection graph

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)^p S_i = S. The intersection graph of F is denoted Ω(F) and defined by V(Ω(F)) = F, with S_i and S_j adjacent whenever i!=j and S_i intersection S_j !=∅. Then a graph G is an intersection graph on S if there exists a family F of subsets for which G and Ω(F) are isomorphic graphs. Graph intersections can be computed in the Wolfram Language using GraphIntersection[g, h].

graph union | intersection number