Which of the following statements about minimum spanning tree is correct?

A minimum spanning tree must have the edge with the smallest weight (In Kruskal’s algorithm we start from the smallest weight edge). So, C is TRUE.

What are the properties of minimum spanning tree?

Properties. If there are n vertices in the graph, then each spanning tree has n − 1 edges. If each edge has a distinct weight then there will be only one, unique minimum spanning tree. If the weights are positive, then a minimum spanning tree is in fact a minimum-cost subgraph connecting all vertices.

Which is not the property of a minimum spanning tree?

If G(V, E) is a graph then every spanning tree of graph G consists of (V – 1) edges, where V is the number of vertices in the graph and E is the number of edges in the graph. So, (E – V + 1) edges are not a part of the spanning tree.

Does the lowest weight edge in every cycle have to belong to the MST?

does every MST of G contains the minimum weighted edge? Yes. MSTs have a cut property. A cut is simply a partition of the vertices of the graph into two disjoint sets.

Which of the following statement is always correct for any two spanning tree?

Narrowing the scope further: I shall only consider graphs with no loops and with no multiple edges – in what follows a pair of vertices may be connected with at most one edge. Hence, the right answer is option 2 “Selected vertices have same degree”

Which one of the following statements about minimum spanning tree is incorrect?

Edge CD is edge with minimum weight and edge AB is edge with maximum weight. And G has a unique minimum spanning tree is also true because the graph has edges with distinct weights. So, no minimum spanning tree contains AB is false.

Which of the following is not a minimum spanning tree algorithm?

9. Which of the following is not the algorithm to find the minimum spanning tree of the given graph? Explanation: The Boruvka’s algorithm, Prim’s algorithm and Kruskal’s algorithm are the algorithms that can be used to find the minimum spanning tree of the given graph.

What is a minimum spanning tree Geeksforgeeks?

A minimum spanning tree (MST) or minimum weight spanning tree for a weighted, connected, undirected graph is a spanning tree with a weight less than or equal to the weight of every other spanning tree. The weight of a spanning tree is the sum of weights given to each edge of the spanning tree.

What is the weight of minimum spanning tree?

A spanning tree with assigned weight less than or equal to the weight of every possible spanning tree of a weighted, connected and undirected graph G, it is called minimum spanning tree (MST). The weight of a spanning tree is the sum of all the weights assigned to each edge of the spanning tree.

Does every weighted graph have a minimum spanning tree?

More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components. There are many use cases for minimum spanning trees.