Question

using vertices to represent land masses and edges to represent bridges, which graph models the layout of the city shown in the map? the city of gothamville let a, b, c represent the islands as shown, and n, s represent the north and south sides of the river. choose the correct graph below.

Explanation:

Step1: Analyze the connections

• Check the number of bridges (edges) between each land - mass (vertex).
• For example, count how many bridges connect North Gothamville (N) to other land - masses.

Step2: Match with the graph

• Look at the first graph:
• Check the connections of vertex \(A\), \(B\), \(C\), \(N\), \(S\).
• Count the number of edges from each vertex.
• For the second graph:
• Notice that in the map, \(A\) is connected to \(B\) and \(S\) (assuming based on bridge - landmass relationship). But in the second graph, the connections are different.

Answer:

The first graph (the one with vertices \(A\), \(B\), \(C\), \(S\), \(N\) where the connections match the bridge - landmass relationships in the map) is the correct one.