Abstract
The intersection number of a digraph D is the minimum size of a set U, such that D is the intersection digraph of ordered pairs of subsets of U. The paper describes much of the work done in the area of intersection graphs and digraphs, and proves two main results: Theorem 1 The intersection number of the line digraph of D equals the number of vertices of D that are neither sources nor sinks. Theorem 2 If D contains no loops, the intersection numbers of total digraph, middle digraph and subdivision digraph of D are all equal to the number of vertices of D that are not sources, added to the number of vertices of D that are not sinks.
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