mgf1107lecture20

mgf1107lecture20 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 20 Spanning Trees In the previous lecture we looked at the definition of a tree in graph theory, and the properties that they have. A more realistic problem though is how to create trees from connected graphs that are initially not trees, and in particular how to create one that minimizes cost or distance. Definition: Given any network, the number of redundant edges is equal to M – (N – 1), where M is the number of edges, and N is the number of vertices. Definition: A spanning tree of a graph G is a selection of edges that form a tree and include every vertex. Note: In order to create a spanning tree we must remove a number of edges equal to the redundancy of the original network. Ex.
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The problems become more interesting when we have a preference for one spanning tree over another based on cost or distance due to the weighting of the edges Definition: A minimum spanning tree (MST) is a a spanning tree with weight less than or equal to the weight of every other spanning tree. Ex.
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mgf1107lecture20 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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