00:02
We're given a weighted graph and we're asked to use kruskull's algorithm to find a minimum spanning tree for this graph.
00:10
The graph is the one from exercise 4 in the book.
00:13
This is a graph on vertices, a, b, c, d, e, f, g, h, i -j -k -l -m -n -o -p with weighted edges.
00:22
So i'd refer you to the book to see the vertices with their weighted edges.
00:27
I have not drawn the weighted edges.
00:28
It's too complicated, i feel like.
00:31
But inaccurate pictures in the book.
00:35
Use cruistols algorithm, what we're going to do.
00:38
The first step is to simply draw the graph, which has the vertices of our weighted graph.
00:43
So i've drawn here vertices a through p.
00:49
The next step in the algorithm is to find the edges with the smallest weights.
00:56
So the smallest weights in the given graph is 1.
00:58
And this belongs to the edges ab, a -e, c -d, and d -h.
01:05
So first let's add ab.
01:11
We don't create a circuit, so this is valid.
01:13
Let's add the edge ae.
01:16
We don't create a circuit, so this is valid.
01:19
Let's add the edge cd.
01:22
This does not create a circuit, so it's valid.
01:26
Add the edge dh.
01:28
This does not create a circuit, so it's also valid.
01:35
Now, in the remaining graph, the smallest weight is 2.
01:41
And so we want to consider all the edges of weight 2 that don't cause a circuit to be added to the graph.
01:48
So first consider, say, edge am...