Understand spanning tree and minimum spanning tree

    In this tutorial, you will learn about spanning tree and minimum spanning tree through examples and diagrams.
    Before learning spanning tree, we need to understand two graphs: undirected graph and connected graph.
    An undirected graph is a graph whose edges do not point in any direction (that is, the edges are bidirectional).

    An undirected graph is a
    graph that always has a path from a vertex to any other vertex.

    Connected graph

Spanning tree

    The spanning tree is a subgraph of an undirected connected graph, which contains all the vertices of the graph and the smallest possible number of edges. If a vertex is missing, it is not a spanning tree.
    The side may have weight, or it may not.
    A spanning tree can be created from a complete graph. The total number of spanning trees with n vertices is equal to $n^{(N-2)}$ .
    If n=4, the maximum possible number of spanning trees is equal to$4^{4-2}=16$ . Therefore, a complete graph with 4 vertices can form 16 spanning trees.

Spanning tree example

    Let us use the following example to understand the spanning tree: The
    original diagram is:

    some possible spanning trees that can be created from the above diagram are:

Minimum spanning tree

    The minimum spanning tree is the spanning tree that is as small as possible for the sum of the weights of the edges.

Minimum spanning tree example

    Let us understand the above definition through the following example.
    The initial graph is:

    weighted graph. The
    possible spanning tree in the figure above is:




    the minimum spanning tree of the above spanning tree is: the minimum spanning tree

    in the graph can be found using the following algorithm:

1. Prim’s Algorithm
2. Kruskal’s Algorithm

Spanning Tree Application

• Computer network routing protocol
• Cluster analysis
• Civil network planning

Minimum spanning tree application

• Find the route on the map
• Design telecommunication networks, water supply networks, power grids and other networks.

Reference documents

[1]Parewa Labs Pvt. Ltd.Spanning Tree and Minimum Spanning Tree[EB/OL].https://www.programiz.com/dsa/spanning-tree-and-minimum-spanning-tree,2020-01-01.