Exploring Minimum Spanning Trees in Algorithms

What is a minimum spanning tree?

• A tree that has no edges.

• A tree that spans only a subset of vertices.

• A tree that spans all vertices with the minimum possible weight.

• A tree that spans all vertices with the maximum possible weight.

What is required for a graph to have a minimum spanning tree?

• All edges must have a certain value assigned to them.

• The graph must have no cycles.

• All edges must have the same value.

• The graph must be a complete graph.

How do you calculate the weight of a spanning tree?

• By multiplying the values of all edges.

• By summing the values of all edges.

• By summing the values of all vertices.

• By counting the number of edges.

If a spanning tree has edges with values 2, 4, 3, 2, 3, and 6, what is its weight?

• 22

• 21

• 20

• 18

What is the weight of a spanning tree with edges valued at 3, 4, 3, 2, 3, and 6?

• 22

• 20

• 18

• 21

What defines a minimum spanning tree?

• It has the maximum possible sum of edge values.

• It has no edges.

• It has the smallest possible sum of edge values.

• It has the same sum of edge values as any other spanning tree.

Can a graph have more than one minimum spanning tree?

• Yes, but they must have the same weight.

• No, it must have at least three.

• Yes, but they must have different weights.

• No, it can only have one.

What is a key property of every minimum spanning tree?

• The sum of the edges is as high as possible.

• The sum of the edges is as low as possible.

• It has the same number of edges as the original graph.

• It includes all possible edges.