Aspire Faculty ID #19287 · Topic: UGC NET Computer Science June 2019 (Paper II) · Just now
UGC NET Computer Science June 2019 (Paper II)

Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a real-valued function $f:V\times V\to R$:

$P_1$: For all $u,v\in V,\ f(u,v)=-f(v,u)$

$P_2$: $\sum_{v\in V} f(u,v)=0$ for all $u\in V$

Which one of the following is/are correct?

Solution

Property $P_1$ is the skew-symmetry property of flow.

So, $P_1$ is correct.

Property $P_2$ represents flow conservation, but in a flow network, flow conservation holds for all vertices except the source and sink.

The statement says it holds for all $u\in V$, which is not correct.

So, $P_2$ is false.

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