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286. Introduction to Minimum Spanning Tree (MST)
What is a Spanning Tree?
In an undirected and connected graph G=(V,E), a spanning tree is a subgraph that is a tree which includes all of the vertices of G, with minimum possible number of edges. A graph may have several spanning trees. The cost of the spanning tree is the sum of the weights of all the edges in the tree
What is a Minimum Spanning Tree?
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edgeweighted (un)directed graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. Number of edges in MST: V1 (V – no of vertices in Graph).
Example:
Algorithms for finding the Minimum Spanning Tree:
Applications:
Minimum spanning trees have direct applications in the design of networks, including computer networks, telecommunications networks, transportation networks, water supply networks, and electrical grids. Also used in
 Approximating travelling salesman problem
 Approximating multiterminal minimum cut problem
 Approximating minimumcost weighted perfect Cluster Analysis
 Handwriting recognition
 Image segmentation
 Circuit design
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