Table of Contents

## What are the properties of spanning tree?

General Properties of Spanning Trees: All the possible spanning trees of a graph have the same number of edges and vertices. A spanning tree can never contain a cycle. Spanning tree is always minimally connected i.e. if we remove one edge from the spanning tree, it will become disconnected.

## What is the importance of minimal spanning tree?

Minimum spanning trees are used for network designs (i.e. telephone or cable networks). They are also used to find approximate solutions for complex mathematical problems like the Traveling Salesman Problem. Other, diverse applications include: Cluster Analysis.

**What are the features of minimum spanning tree?**

The properties of a minimum spanning tree are:

- Possible multiplicity. If there are n vertices in the graph, then each spanning tree has n − 1 edges.
- Uniqueness.
- Minimum-cost subgraph.
- Cycle property.
- Cut property.
- Minimum-cost edge.
- Contraction.

### What is the time complexity of spanning tree?

When we implement this algorithm using adjacency matrix and without using priority queue, the time complexity comes out to be O(V^2), where V is the total no. of vertices and E is the total no. of edges.

### What do you understand by minimum spanning tree explain how minimum cost spanning tree is computed?

A minimum spanning tree can be defined as the spanning tree in which the sum of the weights of the edge is minimum. The weight of the spanning tree is the sum of the weights given to the edges of the spanning tree.

**What is spanning and minimum spanning tree?**

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

## Are minimum spanning trees unique?

Note that we use minimum spanning tree as short for minimum weight spanning tree. Weight of MST is 4 + 8 + 7 + 9 + 2 + 4 + 1 + 2 = 37 • Note: MST is not unique: e.g. (b, c) can be exchanged with (a, h) 1 Page 2 The MST problem is considered one of the oldest, fundamental problems in graph algorithms.

## Which of the following statements about the minimum spanning tree is correct?

A minimum spanning tree must have the edge with the smallest weight (In Kruskal’s algorithm we start from the smallest weight edge). So, C is TRUE.