Graphs and Networks 1 (AQA A-Level Further Maths): Flashcards

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Network Flows 1
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Capacity in a capacitated network

Maximum possible flow along an arc

Source node (S)

Node where flow enters; all arcs directed away from it

Sink node (T)

Node where flow exits; all arcs directed towards it

Feasibility condition

Flow in an arc \leq capacity

Conservation condition

At intermediate nodes: total inflow = total outflow

Value of the flow

Total outflow from S = total inflow to T

Saturated arc

Arc where flow = capacity (at full capacity)

Unsaturated arc

Arc where flow < capacity (has spare capacity)

Cut in a network

Set of arcs separating S and T when removed

Maximum flow-minimum cut theorem

Max flow value = min cut capacity

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