00:01
Hello students, to solve the travelling problem for the given graph, we need to find the total weight of all hamilton circuits to determine the circuit with the minimum total weight.
00:10
Given ab equal to 70, bc equal to 15, ac equal to 20, ad equal to 30, bd equal to 50 and cd equal to 10.
00:27
To find the total weight of all hamilton circuits, we need to consider all possible circuits that visit each vertex exactly once.
00:35
There are three possible hamilton circuits.
00:39
Those are, the first one is a to b to c to d to a.
00:54
The second one is a to d to c to b to a.
01:01
And the third one is a to b to d to c to a.
01:08
Let's calculate the total weight of each circuit.
01:11
So, for the first one, a to b, b to c, c to d to a.
01:21
So, total weight equal to ab plus bc plus cd plus da.
01:33
We know ab equal to 70 plus 15 plus 10 plus 30.
01:39
That is equal to 125.
01:41
Now, moving for the second one, a to d to c to b to a.
01:48
So, total weight equal to ad plus dc plus cb plus ba.
01:57
That is equal to 30 plus 10 plus 15 plus 70.
02:01
That is equal to 125.
02:09
Now, the third one, a to b to d to c to a.
02:18
Total weight equal to 70 plus 50 plus 10 plus 20.
02:30
That is equal to 150.
02:32
Therefore, we need to find the minimum total weight.
02:37
We can see 1 and 2 have the same total weight.
02:41
That is 125 and 125 which is less than the third total weight.
02:46
That is 150.
02:47
Hence, the circuit with the minimum total weight is either a to b to c to d to a or a to d to c to b to a.
03:21
Both with a total weight of 125.
03:35
Now, moving forward to the second bit, determine the minimum spanning tree...
