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You are analyzing a transportation network graph that represents road connections between cities. To simplify your analysis and reduce computation time, you decide to apply an elementary graph operation. Which operation would you use, and why?a)Deletion, to remove unnecessary cities and roads from the graph.b)Enumeration, to list all road connections for statistical analysis.c)Contraction, to merge closely connected cities into one for simplification.d)Addition, to create new road connections between cities to improve navigatio

Question

You are analyzing a transportation network graph that represents road connections between cities. To simplify your analysis and reduce computation time, you decide to apply an elementary graph operation. Which operation would you use, and why?a)Deletion, to remove unnecessary cities and roads from the graph.b)Enumeration, to list all road connections for statistical analysis.c)Contraction, to merge closely connected cities into one for simplification.d)Addition, to create new road connections between cities to improve navigatio

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Solution

The operation you would use is c) Contraction. This operation allows you to merge closely connected cities into one, simplifying the graph and reducing computation time. This is particularly useful when the exact details of the road connections between these closely connected cities are not important for the overall analysis of the transportation network. By treating these closely connected cities as a single node in the graph, you can more easily analyze the larger structure and connectivity of the network.

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