# Which of the following are the applications of spanning trees?

## Which of the following are the applications of spanning trees?

Applications. Minimum spanning trees have direct applications in the design of networks, including computer networks, telecommunications networks, transportation networks, water supply networks, and electrical grids (which they were first invented for, as mentioned above).

## What is the weight of the minimum spanning?

The weight of a spanning tree is the sum of weights given to each edge of the spanning tree. How many edges does a minimum spanning tree has? A minimum spanning tree has (V – 1) edges where V is the number of vertices in the given graph.

**Which algorithm are used to construct spanning tree?**

Because the minimum spanning tree problem is very important in network optimization, researchers have conducted a detailed study of this problem. At present, there are already some classical algorithms for solving the minimum spanning tree in graph theory, such as Kruskal algorithm or Prim algorithm.

### What is the definition of a minimum spanning tree?

What is a Minimum Spanning Tree? A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted directed or undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

### How to make a spanning tree with a smaller weight?

As e1 and e2 are part of the cycle C, replacing e2 with e1 in B therefore yields a spanning tree with a smaller weight. This contradicts the assumption that B is a MST.

**Which is the highest weighted edge in a spanning tree?**

A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree (or MBST) if the graph does not contain a spanning tree with a smaller bottleneck edge weight. A MST is necessarily a MBST (provable by the cut property ), but a MBST is not necessarily a MST.

## How is a spanning tree different from a connected graph?

A spanning tree is a sub-graph of an undirected connected graph, which includes all the vertices of the graph with a minimum possible number of edges. If a vertex is missed, then it is not a spanning tree. The edges may or may not have weights assigned to them.