What Is Spanning Tree in Data Structure With Example?
In the field of computer science and data structures, a spanning tree is a special type of connected acyclic graph. It is derived from a given graph and contains all the vertices of the graph. A spanning tree has the minimum possible number of edges that are required to connect all the vertices.
A graph is a collection of nodes (also known as vertices) connected by edges. Each edge represents a relationship or connection between two nodes. A graph can be represented visually as a set of points (vertices) connected by lines (edges).
A spanning tree can be useful in various applications, such as network design, as it helps to create an efficient and minimal structure for connectivity.
Properties of Spanning Trees:
- A spanning tree must include all the vertices from the original graph.
- A spanning tree cannot contain any cycles, which means there should be no repeated edges or loops.
- A spanning tree must have exactly n-1 edges, where n is the number of vertices in the original graph.
Let’s consider an example to understand how to find a spanning tree for a given graph.
We have a graph with 5 vertices: A, B, C, D, and E. The edges are represented by lines connecting these vertices.
To find a spanning tree for this graph, we need to ensure that it satisfies all the properties mentioned earlier. One possible spanning tree for this example could be:
In this spanning tree, we have exactly 4 edges (n-1) connecting all the vertices without any cycles. It covers all the nodes of the original graph and provides a minimal structure for connectivity.
A spanning tree is a crucial concept in data structures and graph theory. It helps in creating an efficient and minimal structure to connect all the vertices of a graph. By understanding the properties and examples of spanning trees, you can apply this knowledge in various applications like network design and optimization.