How do you prove a graph has a unique minimum spanning tree?

If all edge weights in a connected graph G are distinct, then G has a unique minimum spanning tree.

How do you find the minimum spanning tree of a weighted graph?

Step 1 − Arrange all the edges of the given graph G(V,E) in ascending order as per their edge weight. Step 2 − Choose the smallest weighted edge from the graph and check if it forms a cycle with the spanning tree formed so far. Step 3 − If there is no cycle, include this edge to the spanning tree else discard it.

How many number of minimum spanning trees are possible for a given weighted connected graph with distinct weights?

If each edge has a distinct weight, then there will be only one, unique minimum spanning tree. A connected graph G can have more than one spanning trees.

What determines whether a graph has more than one minimum spanning tree?

Remember for a graph to have different MSTs, atleast two edges must be equal .

Does every weighted graph have a unique minimum spanning tree?

Uniqueness. If each edge has a distinct weight then there will be only one, unique minimum spanning tree. This is true in many realistic situations, such as the telecommunications company example above, where it’s unlikely any two paths have exactly the same cost.

What is the minimum number of spanning tree in a connected graph?

Every undirected and connected graph has a minimum of one spanning tree.

How can we make minimum spanning tree and also with example?

A minimum spanning tree is a special kind of tree that minimizes the lengths (or “weights”) of the edges of the tree. An example is a cable company wanting to lay line to multiple neighborhoods; by minimizing the amount of cable laid, the cable company will save money. A tree has one path joins any two vertices.

How do you know how many spanning trees a graph has?

If a graph is a complete graph with n vertices, then total number of spanning trees is n(n-2) where n is the number of nodes in the graph. In complete graph, the task is equal to counting different labeled trees with n nodes for which have Cayley’s formula.

Does it possible to find more than one MST from a particular graph?

The answer would, probably be no ; multiple STs are possible (depends on the graph), but, if each edge has a unique weight , only one MST will be possible.

What makes MST unique?

Another way to think about it: each vertex in G will have at least one incident edge in the MST. Can you say anything about this edge? To keep things simple, we’ll assume that the edge weighst are distinct; that is, for any pair of edges e, e , we have w(e) = w(e ). This guarantees that the MST is unique.