G has a topological order and it also has a cycle.
{"Image DocumentName": "G has a topological order and it also has a cycle.", "Image ImageDescription": "Opposite property. Fact: If graph G has a topological order then it is DAG. Proof: Suppose, to the contrary, that. G has a topological order and it also has a cycle. Let v be the smallest element in the cycle according to the topological order. It follows that its predecessor in the cycle must be smaller (in the final order) than v, but this contradicts the fact that v is the smallest element on the cycle. We get a contradiction with our assumption, which means that G must not have a cycle. Graph Algorithms.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}