Explain how a vertex u of a directed graph can end up in a depth-first tree containing only u, even though u has both incoming and outgoing edges in G.
Answer to relevant QuestionsShow that a depth-first search of an undirected graph G can be used to identify the connected components of G, and that the depth-first forest contains as many trees as G has connected components. More precisely, show how to ...A directed graph G = (V, E) is said to be semi connected if, for all pairs of vertices u, v ¬ V, we have u →v or v→ u. Give an efficient algorithm to determine whether or not G is semi connected. Prove ...Suppose that all edge weights in a graph are integers in the range from 1 to |V|. How fast can you make Kruskal’s algorithm run? What if the edge weights are integers in the range from 1 to W for some constant W?Two flows of air both at 200 kPa of equal flow rates mix in an insulated mixing chamber. One flow is at 1500 K and the other is at 300 K. Find the irreversibility in the process per kilogram of air flowing out.A car air-conditioning unit has a 0.5-kg aluminum storage cylinder that is sealed with a valve and it contains 2 L of refrigerant R-134a at 500 kPa and both are at room temperature 20C. It is now installed in a car ...
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