math - What is the maximum number of possible topological sorts of N-order Direct Acyclic Graph? -


i need find maximum number of topological sorts on direct acyclic graph of n-order. i've checked running depth first search algorithm on various direct acyclic graphs, , looks size of depth first search algorithm forest created after running dfs on graph. or maybe wrong or miss something. need prove it. appreciated. thank you.

if have total of n elements, maximum number of possible ways order n elements n! (the number of permutations of n elements). can't better that. if can find family of graphs n nodes have n! possible topological orderings, know has maximum possible number of topological orderings.

as hint, indeed possible find n-node dags n! possible topological orderings. try thinking mean possible edges between nodes. once you've found family of graphs, it's easy show have maximum possible number of topological orderings using above argument.

hope helps!


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