# Question: Let G V E be a directed graph in which each vertex

Let G = (V, E) be a directed graph in which each vertex u ¬ V is labeled with a unique integer L(u) from the set {1, 2,..., |V|}. For each vertex u ¬ V, let R(u) = (v ε V : u → v) be the set of vertices that are reachable from u. Define min(u) to be the vertex in R(u) whose label is minimum, i.e., min(u) is the vertex v such that L(v) = min {L(w) : w ¬ R(u)}. Give an O (V + E)-time algorithm that computes min(u) for all vertices u ¬ V.

## Answer to relevant Questions

Give a simple example of a graph such that the set of edges {(u, v): there exists a cut (S, V - S) such that (u, v) is a light edge crossing (S, V - S)} does not form a minimum spanning tree.Calculate the reversible work and irreversibility for the process described in Problem 5.65, assuming that the heat transfer is with the surroundings at20C.A steam turbine receives steam at 6 MPa, 800C. It has a heat loss of 49.7 kJ/kg and an isentropic efficiency of 90%. For an exit pressure of 15 kPa and surroundings at 20C, find the actual work and the ...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 ...Nitrogen flows in a pipe with velocity 300 m/s at 500 kPa, 300C. What is its availability with respect to an ambient at 100 kPa, 20C?Post your question