Give a counterexample to the conjecture that if there is a path from u to v in a directed graph G, and if d[u] < d[v] in a depth-first search of G, then v is a descendant of u in the depth-first forest produced.
Answer to relevant QuestionsGive a counterexample to the conjecture that if there is a path from u to v in a directed graph G, then any depth-first search must result in d[v] ≤ f[u].Give an O (V + E)-time algorithm to compute the component graph of a directed graph G = (V, E). Make sure that there is at most one edge between two vertices in the component graph your algorithm produces.Show that a graph has a unique minimum spanning tree if, for every cut of the graph, there is a unique light edge crossing the cut. Show that the converse is not true by giving a counterexample.An air compressor takes air in at the state of the surroundings 100 kPa, 300 K. The air exits at 400 kPa, 200C at the rate of 2 kg/s, determine the minimum compressor work input.Air flows through a constant pressure heating device, shown in Fig. P10.15. It is heated up in a reversible process with a work input of 200 kJ/kg air flowing. The device exchanges heat with the ambient at 300 K. The air ...
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