## What is minimum cost spanning tree explain 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 calculate the cost of minimum spanning tree?

Given an undirected graph of V nodes (V > 2) named V1, V2, V3, …, Vn. Two nodes Vi and Vj are connected to each other if and only if 0 < | i – j | ≤ 2. Each edge between any vertex pair (Vi, Vj) is assigned a weight i + j. The task is to find the cost of the minimum spanning tree of such graph with V nodes.

#### How do you find minimum spanning tree explain the Krushkal’s algorithm with example?

Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2

1. Sort all the edges in non-decreasing order of their weight.
2. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge.
3. Repeat step#2 until there are (V-1) edges in the spanning tree.

What is minimum cost spanning tree explain?

Minimum Spanning Tree is a Spanning Tree which has minimum total cost. If we have a linked undirected graph with a weight (or cost) combine with each edge. Then the cost of spanning tree would be the sum of the cost of its edges.

Is a minimum spanning tree unique?

Any undirected, connected graph has a spanning tree. If the graph has more than one connected component, each component will have a spanning tree (and the union of these trees will form a spanning forest for the graph). The spanning tree of G is not unique. This is called the minimum spanning tree (MST) of G.

## What is minimum spanning tree and its properties?

A Minimum Spanning Tree(MST) or minimum weight spanning tree for a weighted, connected, undirected graph is a spanning tree having a weight less than or equal to the weight of every other possible spanning tree. The weight of a spanning tree is the sum of weights given to each edge of the spanning tree.

### What are the applications of minimum spanning tree?

Other practical applications based on minimal spanning trees include: Taxonomy. Cluster analysis: clustering points in the plane, single-linkage clustering (a method of hierarchical clustering), graph-theoretic clustering, and clustering gene expression data. Constructing trees for broadcasting in computer networks.

#### Is Prims faster than Kruskal?

Prim’s algorithm gives connected component as well as it works only on connected graph. Prim’s algorithm runs faster in dense graphs. Kruskal’s algorithm runs faster in sparse graphs.

Is Kruskal greedy?

Unsourced material may be challenged and removed. Kruskal’s algorithm finds a minimum spanning forest of an undirected edge-weighted graph. It is a greedy algorithm in graph theory as in each step it adds the next lowest-weight edge that will not form a cycle to the minimum spanning forest.

Does minimum spanning tree give shortest path?

Minimum spanning tree is a tree in a graph that spans all the vertices and total weight of a tree is minimal. Shortest path is quite obvious, it is a shortest path from one vertex to another.

## Which is greedy algorithm for minimum spanning tree?

We have discussed Kruskal’s algorithm for Minimum Spanning Tree. Like Kruskal’s algorithm, Prim’s algorithm is also a Greedy algorithm. It starts with an empty spanning tree. The idea is to maintain two sets of vertices. The first set contains the vertices already included in the MST, the other set contains the vertices not yet included.

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

What is a Minimum Spanning Tree? The cost of a spanning tree is the total of the weights of all the edges in the tree. For example, the cost of spanning tree in Fig. 3 is (2+4+6+3+2) = 17 units, whereas in Fig. 4 it is (2+3+6+3+2) = 16 units.

#### How to create a minimum spanning tree with Kruskal?

1 Sort all the edges in non-decreasing order of their weight. 2 Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed,… 3 Repeat step 4 2 until there are (V-1) edges in the spanning tree. More

Can a graph have more than one spanning tree?

A single graph can have many different spanning trees. A minimum spanning tree (MST) or minimum weight spanning tree for a weighted, connected, undirected graph is a spanning tree with a weight less than or equal to the weight of every other spanning tree. The weight of a spanning tree is the sum of weights given to each edge of the spanning tree.