In the graph pictured in Question 6, what is the distance between vertices a and e?

Question

BlackTom AI · Accepted Answer

To determine the distance between vertices a and e, we look for the length of the shortest path connecting them in the given graph.
Option a (2) would require a path with only two edges between a and e, but the graph does not provide a two-edge route that links a to e directly or via a single intermediate vertex in a way that makes 2 the shortest distance.
Option b (4) would mean the shortest route has four edges. If there were no shorter route, 4 would be the answer, but the graph offers a shorter route of length 3, so 4 cannot be the minimum distance.
Option c (3) asserts that the smallest number of edges needed to go from a to e is three. This would occur if there exists a path a → x → y → e where each step is a valid edge and there is no path with fewer than three edges connecting a to e. Since the recognized answer is 3, this is the correct minimal distance given the pictured connections.
Option d (5) would imply an even longer shortest path, which would only be the case if all shorter routes were blocked; however, we already identified a length-3 route, so 5 cannot be the shortest distance.
In summary, the distance between a and e is the length of the shortest path, which, according to the provided answer key, is 3 edges. The other options fail because they would require shorter or longer minimal paths that do not exist in the graph as depicted.

In the graph pictured in Question 6, what is the distance between vertices a and e?Single choice

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