Can there be more than one spanning tree?

A connected graph G can have more than one spanning tree. All possible spanning trees of graph G, have the same number of edges and vertices. Removing one edge from the spanning tree will make the graph disconnected, i.e. the spanning tree is minimally connected.

How many minimum spanning trees can be formed from a given graph?

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

Does every graph have only one spanning tree?

Every graph has only one minimum spanning tree. Explanation: Minimum spanning tree is a spanning tree with the lowest cost among all the spacing trees. Sum of all of the edges in the spanning tree is the cost of the spanning tree. There can be many minimum spanning trees for a given graph.

How many spanning trees does the following graph have?

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.

Is MST NP complete?

The fact that the k-MST problem is NP-complete for distance matrices in [RT], but polynomially solvable, when the distance matrix is in [RI], points out an interesting difference between these two at first sight similar problems.

Can the highest weight edge in G be in the MST?

Does a MST contain the maximum weight edge? Sometimes, Yes. It depends on the type of graph. If the edge with maximum weight is the only bridge that connects the components of a graph, then that edge must also be present in the MST.

How many spanning trees are possible for the graph?

How many spanning trees does complete graph K5 has?

Let G = K5, the complete graph on five vertices. A simple counting argument shows that K5 has 60 spanning trees isomorphic to the first tree in the above illustration of all nonisomorphic trees with five vertices, 60 isomorphic to the second tree, and 5 isomorphic to the third tree.