The complement of a digraph has the same vertex set as the original digraph,and an arc

Chapter 3, Problem 17

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The complement of a digraph has the same vertex set as the original digraph,and an arc from x to y exactly when the original digraph does not have an arcfrom x to y. The two digraphs shown below are complementary. Call adigraph symmetric (transitive) its relation is symmetric (transitive). a) Show that the complement of a symmetric digraph is symmetric.(b) Show by example that the complement of a transitive digraph need notbe transitive.

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