Please write it in detail. Suppose that G = (V, E) is a directed graph with |V| = n and JE| = m unlessotherwise stated. Also suppose that all edge capacities are integral and that there are nodirected 2-cycles.Then consider the following network (G, u, s, t) with edge capacities given by the labels8810712111(a) Run the Ford-Fulkerson algorithm to find a maximum flow ƒ* . Be sure to give the flowf and corresponding residual graph G, after each iteration.(b) Define S := {v€ V | there exists an s – v path in G; } . What is S, and what is the valueu(6* (S)) of the cut?

Answered: lease write it in det

Math

Advanced Math

lease write it in det

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 80EQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Please write it in detail.

Suppose that G = (V, E) is a directed graph with |V| = n and JE| = m unless
otherwise stated. Also suppose that all edge capacities are integral and that there are no
directed 2-cycles.
Then consider the following network (G, u, s, t) with edge capacities given by the labels
8
8
10
7
12
11
1
(a) Run the Ford-Fulkerson algorithm to find a maximum flow ƒ* . Be sure to give the flow
f and corresponding residual graph G, after each iteration.
(b) Define S := {v€ V | there exists an s – v path in G; } . What is S, and what is the value
u(6* (S)) of the cut?

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