(a)
To prove: The law of conservation of flow at a andat e.
(a)
Explanation of Solution
Proof:
WE have given a directed network set V, the capacity of arc uv denoted
At a,
(b)
The value of the indicated flow;
(b)
Explanation of Solution
It is well known that, the value of flow
That the net amount of flow per unit time leaving the source or, entering the sink.
(c)
The capacity of the
(c)
Explanation of Solution
He capacity of an
Therefore, the capacity of the cut is
(d)
The flow be increased along the path sbft.
(d)
Explanation of Solution
No, the flow cannot be increased along the path sbft because, this path contains bf the saturated arc.
(e)
Whether the “given flow maximum” or not.
(e)
Explanation of Solution
The
Therefore the flow is not maximum.
Want to see more full solutions like this?
Chapter 14 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage