Quiz - MO412 - Julia Pietro

According to Kuratowski’s Theorem, for connected and planar networks, the number of vertices minus the number of edges plus the number of faces equals 2. This is Euler’s Formula, where:  V - E + F = 2.  Considering that faces are the regions bounded by links and that there will always be an outer face, given the following situations, how would Euler’s Formula behave? Scenario 01: a single node A.  Scenario 02: addition of a node B with a link to this existing node A. Scenario 03: addition of another node C with a link to the existing node A.  Scenario 04: addition of a link between nodes B and C.  a.) Euler’s formula remains constant (equal to 2) in scenarios 01 and 02.  b.) Euler’s formula remains constant (equal to 2) in all scenarios. c.) Euler’s formula depends on the number of nodes; therefore, it takes on a different value for each scenario: Scenario 01 = 2; Scenario 02 = 2; Scenario 03 = 3; and Scenario 04 = 3 d.) Euler’s formula depends on the nu...

Consider that on Easter Sunday, due to high demand, airlines had to limit the number of planes that could fly over certain regions. Help Azul Airlines maximize the number of planes that could travel on April 4, 2026, at 2 PM, through the areas shown in the figure below. What would be the residual network formed from the networks in Figure 2?  SP is the source node and AM is the sink node.  1: 2:  a.)  b.)  c.)  d.)  e) None of the above Original idea by: Julia de Pietro Bigi