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Spanning Trees and Dijkstra’s Algorithm. Excursions in Modern Mathematics( Tannenbaum ) and Thinking Mathematically (Blitzer). Spanning Trees. A subgraph that connects all the vertices of the network and has no circuits .

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Spanning trees and dijkstra s algorithm

Spanning Trees and Dijkstra’s Algorithm

Excursions in Modern Mathematics(Tannenbaum) and Thinking Mathematically (Blitzer)


Spanning trees
Spanning Trees

A subgraph that connects all the vertices of the network and has no circuits.

By removing redundant edges makes it possible to increase the efficiency of the network modeled by the graph.

A spanning tree must have one less edge than it’s vertices. Number of vertices – 1.



Minimum spanning tree
Minimum Spanning Tree

The minimum cost spanning tree for a weighted graph is a spanning tree with the smallest possible total weight.


Example
Example

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35

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Dijkstra s shortest path algorithm
Dijkstra’s Shortest-Path Algorithm

http://www.youtube.com/watch?v=EMmSL2Jd_nc


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