Consider a minimal spanning tree problem in which pipe must be laid to connect sprinklers on a golf course.When represented with a network,
A)the pipes are the arcs and the sprinklers are the nodes.
B)the pipes are the nodes and the sprinklers are the arcs.
C)the pipes and the sprinklers are the tree.
D)each sprinkler must be connected to every other sprinkler.

Question

Quizplus · Accepted Answer

In a minimal spanning tree problem, we are looking for the shortest possible path that connects all the nodes in a network. In this case, the pipes serve as the connections between the sprinklers (nodes), so we represent them as arcs in the network. Therefore, choice A is the best choice. Choice B is incorrect because it implies that the sprinklers serve as the connections, rather than the pipes. Choice C is incorrect because a tree is a specific type of network that has certain properties, and we cannot assume that the pipes and sprinklers alone form a tree. Choice D is incorrect because it implies that every sprinkler must be directly connected to every other sprinkler, which may not be the case in a minimal spanning tree.

Consider a Minimal Spanning Tree Problem in Which Pipe Must