00:01
I have a couple discrete math problems here.
00:02
First of all, which of these graphs are trees? we've got four graphs here.
00:06
Let's see, so first, v is a, b, c, d, e.
00:08
So we're going to have a, b, c, d, e.
00:14
These are our vertices.
00:16
And edges here is the a goes to b.
00:19
I'm going to make this a little bit thicker.
00:22
A goes to b, a goes to e, b goes to c, c goes to d, and d goes to e.
00:34
Is this a tree? i'm going to claim it's not a tree.
00:37
We can see if we move c over here, a goes to b, b goes to c, c goes to d, d goes to e, and a goes to e.
00:47
This is a loop.
00:49
Loops are not allowed in trees, so a is not a tree.
00:56
So again, for this next one, a, b, c, d, e again.
01:01
A, b, c, d, e.
01:05
You'll be able to leave them out here.
01:07
The edges are a to b, b to c, c to d, d to e.
01:15
This is a tree.
01:16
There are no loops.
01:16
It's just a, what do they call that, a path graph, a line graph.
01:22
Whatever the case, it is a tree.
01:24
There's only one path between any two given nodes, vertices.
01:30
So it's a path.
01:31
There are no loops.
01:32
It's a tree.
01:34
Now a, b, c, d, e again.
01:35
Now we've got a, b, a, c, a, d, and a, e is a tree.
01:40
We can see that's a root node of a, and then just some leaves of b, c, d, and e.
01:44
In particular, there are no loops.
01:46
All that we need for a tree is to be connected and have no loops.
01:51
And it is all connected.
01:52
So we're good.
01:53
That is a tree.
01:55
Finally, we have a, b, c, d, e with a, b, a, c, and d, e.
02:00
This is not a tree.
02:01
Even though there are no loops, it's not connected.
02:04
I can draw this line here that separates the graph into this a, b, c, and the d, e.
02:10
It's not connected and therefore not a tree.
02:15
There is not a unique path from a to d because there is no path from a to d at all...