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Mathematics, 05.05.2020 06:13, Jennifer2019
If G is a DAG we denote by Ο (G) the number of distinct topological sorts of G. Now let G = (V, E) be any DAG. An add-one-vertex operation on G constructs a digraph G 0 = (V 0 , E 0 ) such that β’ G 0 is also a DAG. β’ We add exactly one new vertex, call it z that is, V 0 = V βͺ {z}, z β / V . β’ We add some (possibly 0) new directed edges, that is, E 0 β E. (a) Prove that for any DAG G = (V, E) there is a way to perform an add-one-vertex operation on G such that the resulting DAG G 0 has the same number of topological sorts, i. e. Ο (G 0 ) = Ο (G). (b) Prove that for any DAG G there is a way to perform an add-one-
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If G is a DAG we denote by Ο (G) the number of distinct topological sorts of G. Now let G = (V, E) b...
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