2. Minimum Cost Spanning Trees
The chapter discusses the concept of Minimum Cost Spanning Trees in graph theory, highlighting the importance of connectivity and cost-effectiveness in restoring road networks after disasters. It introduces examples of spanning trees, the criteria for formation, and presents Prim’s and Kruskal’s algorithms as solutions for finding minimum cost spanning trees. The properties and definitions of trees are explored, establishing their fundamental characteristics such as connectivity and acyclicity.
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What we have learnt
- A tree is defined as a connected acyclic graph.
- Any tree with n vertices has exactly n - 1 edges.
- Minimum Cost Spanning Trees can be constructed using Prim’s and Kruskal’s algorithms.
Key Concepts
- -- Minimum Cost Spanning Tree
- A spanning tree of a graph that has the least total edge weight.
- -- Prim's Algorithm
- A greedy algorithm that builds a minimum spanning tree by starting from a vertex and incrementally adding the lowest weight edges.
- -- Kruskal's Algorithm
- A greedy algorithm that builds a minimum spanning tree by adding edges in the order of their weight, ensuring no cycles are created.
- -- Connected Graph
- A graph in which there is a path between every pair of vertices.
- -- Acyclic Graph
- A graph that does not contain any cycles or loops.
Additional Learning Materials
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