I'm in year 11 and my question is regarding a certain topic that I've come across in my curriculum. The problem surrounding this question is about creating a path of minimum length that covers each edge starting and ending at the same vertice including the distance if edges need to be repeated twice. The problem involves this graph. (ignore the numbers in red for now)
I have a solution to solve graphs like these but I wanted to know if it is universal and can work with other graphs similar to this one. The solution involves this simple process:
1: Find all vertices with an odd degree (hence the red numbers)
2: Find the minimum length of edges you would add to make each vertice even degree. These edges will essentially be duplicates of the edges that connect those vertices. (For example CE in the network provided would need to be covered in order to make them both even with a length of 3 )
3: Find the sum of those edges, in this case, it would be 28 and 3, giving us 31
4: Find the sum of all edges in the network and add the answer from step 3 to give us the total. In this case 145+31=176
This answer would be the minimum length required to start and end at the same vertice and covering each edge with repeats.
Wanted to know if this works for similar questions.