Maximum flow (Ford-Fulkersons)

Question

Hi I tried to use the algoritm, but im not sure if my answer in correct. I will show the solution and my answer. I got that the maximum flow 32, but the flow on the edges are diffrent in some cases.Is my answer correct also?

Answer 1

Yes, your answer is also correct. If you modify your answer by sending an extra flow of $1$ around the loops $\ a\rightarrow b\rightarrow g \rightarrow h \rightarrow a\ $ and $\ b\rightarrow g \rightarrow d \rightarrow b\ $, thus increasing the flow on the forward edges $\ (a,b)\ $ and $\ (g,d)\ $ by $1$, decreasing it on the backward edges $\ (h,g)$,$\ (a,h)\ $, and $\ (b,d)\ $ by $1$, and on the backward edge $\ (g,b)\ $ by $2$, you'll end up with the answer given in the book. This doesn't change the net flow leaving any node, which remains at $32$ for node $a$, $-32$ for node $z$, and $0$ for all other nodes.