00:01
Consider the following graph with five vertices and eight edges.
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We want to find the total number of spanning trees.
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So first, let's recall what is a spanning tree.
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A spanning tree is an undirected, connected graph with no cycles.
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In other words, it is a subgraph that connects all of the vertices, but with no loops.
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An example is a graph like the z pattern.
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All of the vertices are connected, but we don't have a loop.
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A loop would look like this, for example.
00:47
A loop is my colloquial term, but really we should call this a cycle.
00:56
So let's redraw our graph and attempt to draw all of the spanning trees.
01:08
So let's start with our z pattern, like so.
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We can draw it starting downwards or starting upwards.
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And we can draw the same z pattern on all of the vertices.
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For example, here i started from the left, but we can start from the top instead.
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And draw this pattern.
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Or this pattern.
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So in this z pattern, we can draw a total of four...