Topological sorting and recognition Directed acyclic graph

topological sorting algorithmic problem of finding topological ordering of given dag. can solved in linear time. kahn s algorithm topological sorting builds vertex ordering directly. maintains list of vertices have no incoming edges other vertices have not been included in partially constructed topological ordering; list consists of vertices no incoming edges @ all. then, repeatedly adds 1 vertex list end of partially constructed topological ordering, , checks whether neighbors should added list. algorithm terminates when vertices have been processed in way. alternatively, topological ordering may constructed reversing postorder numbering of depth-first search graph traversal.

it possible check whether given directed graph dag in linear time, either attempting find topological ordering , testing each edge whether resulting ordering valid or alternatively, topological sorting algorithms, verifying algorithm orders vertices without meeting error condition.