Can a graph have more than one MST?

In a graph, there can be more than one spanning trees. What is Minimum Spanning Tree? A Minimum Spanning Tree (MST) is a subset of edges of a connected weighted undirected graph that connects all the vertices together with the minimum possible total edge weight.

Does a graph with distinct edge weights have a unique minimum spanning tree?

If all edge weights in a connected graph G are distinct, then G has a unique minimum spanning tree. Proof: Let G be an arbitrary connected graph with two minimum spanning trees T and T0; we need to prove that some pair of edges in G have the same weight. At least one such edge must exist, because T is a tree.

Can two minimum spanning trees for the same graph have different edge weights?

1 Answer. The sets must have the same weight.

When all edge weights are distinct is the MST of G unique?

If all the edge weights in G are distinct, then G has a unique MST. Proof. If T = (V,S) and T’ = (V,S’) are two distinct MSTs for G, let e = xy be the cheapest edge of G that is in one of T or T’, but not both. (Since all the edge weights are distinct, there is a unique cheapest edge with this property.)

How many different MST Can a graph have?

There is only one minimum spanning tree in the graph where the weights of vertices are different.

What is a graph that has weights of costs associated with its edges?

i) Network is a graph that has weights or costs associated with it. ii) An undirected graph which contains no cycles is called a forest.

Why the minimum spanning tree of a graph may not be unique?

The edge weights may be zero or negative. If the edge weights are all positive, it suffices to define the MST as the subgraph with minimal total weight that connects all the vertices. The edge weights are all different. If edges can have equal weights, the minimum spanning tree may not be unique.

Which of the following is false in the case of minimum spanning tree of a graph G?

Which of the following is false in the case of a spanning tree of a graph G? Explanation: A graph can have many spanning trees. Each spanning tree of a graph G is a subgraph of the graph G, and spanning trees include every vertex of the gram. Spanning trees are always acyclic.

Is the MST for this graph unique?

Any undirected, connected graph has a spanning tree. If the graph has more than one connected component, each component will have a spanning tree (and the union of these trees will form a spanning forest for the graph). The spanning tree of G is not unique. This is called the minimum spanning tree (MST) of G.

Is an MST necessarily unique?

with n vertices, you can leave out exactly one of the edges and still have all of the vertices be connected. Therefore, you have multiple choices to remove the edge with the highest weight to get a MST, so the MST is not unique.

What is the type of graph if all its edges are assigned some data?

Multigraph: If in a graph multiple edges between the same set of vertices are allowed, it is known as Multigraph. In other words, it is a graph having at least one loop or multiple edges.