Consider the directed acyclic graph G$.$ How many topological orderings does it have? What

are they?

Give an algorithm to detect whether a given undirected graph contains a cycle. If the graph

contains a cycle, then your algorithm should output one. $($It should not output all cycles in the

graph, just one of them.$)$ The running time of your algorithm should be $O(m+n)$ for a graph

with $n$ nodes and $m$ edges.