Question

A minimal spanning tree of a graph G is -
A. A spanning subgraph
B. A tree
C. Minimum weights
D. All of the above

Answer 1

Hint: A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a linked, edge-weighted undirected graph that connects all the vertices without any cycles and with the minimum possible total edge weight. For minimum spanning trees, there are quite a few cases of use.

Complete solution:
1.A spanning tree T of an undirected graph G is a subgraph in the mathematical field of graph theory, which is a tree which includes all the vertices of G, with a minimum possible number of edges.
2. A minimal spanning tree of a graph G is:- A spanning tree is a subset of Graph G with a minimum possible number of edges covering all the vertices.
3. A minimum spanning tree or minimum weight spanning tree is a subset of the edges of a connected (un)directed edge-weighted graph that connects all the vertices together, without any cycles and with the minimum total edge weight possible.
4.A spanning subgraph is a subgraph that contains all of the original graph's vertices.

Note:
Minimum spanning trees are used for network designs (i.e. telephone or cable networks). They are also used to identify specific solutions to complicated mathematical problems such as the Traveling Salesman issue. Other applications include the following: Cluster Analysis. Negate the weights of all edges and then apply the MST algorithm rule. That is, multiply all edge weights by multiplying the negative value (-1). To find the minimum spanning tree, apply either Kruskal's or Prim's algorithm. The maximal spanning tree of the graph is the result of the minimum spanning tree.