a) Show the residual graph for the network flow given in answer to part (c). b) What is the bottleneck edge of the path (?, ?3, ?4, ?) in the residual graph you have given in answer to part (d) ? c) Show the network with the flow that results from augmenting the flow based on the path (?, ?3, ?4, ?) of the residual graph you have given in answer to part (d).

Only considering Finite graphs, also note that every flow network has a maximum flow. Which of the following statements are true for all flow networks (G, s, t, c)? • IfG = (V, E) has as cycle then it has at least two different maximum flows. (Recall: two flows f, f' are different if they are different as functions V × V -> R. That is, if f (u, u) + f' (u, v) for some u, v EV. The number of maximum flows is at most the number of minimum cuts. The number of maximum flows is at least the number of minimum cuts. If the value of f is O then f(u, v) = O forallu, U. | The number of maximum flows is 1 or infinity. The number of minimum cuts is finite.

11.Given the following sample of the Web graph:a) Compute the transition matrix M.b) Which node is dead-end and why?c) Compute an updated transition matrix M’ in which the problem with the dead-end nodeis resolved.d) Based on the updated transition matrix M’ that you computed in the previous step,compute another transition matrix M’’ based on the concept of random teleports.Assume β = 0.8.Note: For matrix M’’, you do not have to do the final calculation. Just show how youbuild matrix M’’.

Show the network with the flow that results from augmenting the flow based on the path (?, ?2, ?3, ?1, ?4, ?) of the residual graph you have given in answer to part. Show the residual graph for the network flow given in answer to part. Show the final flow that the Ford-Fulkerson Algorithm finds for this network, given that it proceeds to completion from the flow rates you have given in your answer to part (i), and augments flow along the edges (?,?1,?3,?) and (?,?2,?5,?).

need correct answer please

A gas pipeline is to be constructed to link several towns in the country. Assuming the pipeline construction costs are the same everywhere in the region, the cheapest network formed by the pipelines and the towns as vertices would form: a Hamilton circuit an Euler circuit a minimum length spanning tree a critical path

Create any four deadlock scenarios. Show them with directed graphs.

also find its average path length

Given the flow network below,  1) Draw the residual graph for the flow shown in the figure 2) Add an augmenting path to achieve the final maxflow. 3) Draw the final residual graph reflecting the augment path from 2) You need to submit the residual graphs from 1) and 3) only.

Let G= (V, E) be an arbitrary flow network with source s and sink t, and a positive integer capacity c(u, v) for each edge (u, v)∈E. Let us call a flow even if the flow in each edge is an even number. Suppose all capacities of edges in G are even numbers. Then,G has a maximum flow with an even flow value.