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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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 Spring '08
 EVINSON
 Math, Calculus

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