If any single connection can fail, how many independent routes exist between San Diego and Illinois?

If any single connection can fail, how many independent routes exist between San Diego and Illinois?

• A. 3 routes
• B. 2 routes
• C. 1 route
• D. 4 routes

Answer: (A)

Independent routes are edge-disjoint paths between two locations, meaning they don’t share any single connection. If any single connection can fail, you want enough independent routes so that losing one edge can’t cut off all paths. In this case, there are three independent routes between San Diego and Illinois. Because these paths don’t share a connection, a failure on one edge only disables one route, leaving two routes still usable to connect the cities. That redundancy is why three routes is the appropriate count here.

Independent routes are edge-disjoint paths between two locations, meaning they don’t share any single connection. If any single connection can fail, you want enough independent routes so that losing one edge can’t cut off all paths. In this case, there are three independent routes between San Diego and Illinois. Because these paths don’t share a connection, a failure on one edge only disables one route, leaving two routes still usable to connect the cities. That redundancy is why three routes is the appropriate count here.