d1 chinese postman

for parts c of question 5 on this paper:

http://www.mrbartonmaths.com/resources/A%20Level%20Past%20Papers/Decision%201/2011%20-%20Jan/D1%20Jan%202011%20worked%20solutions.pdf

i dont understand the solution.

how do you know the number of times a vertex occurs in a chinese postman route?

thanks

It's been a while since I took decision maths, but it was with AQA. I believe it's because you have your optimum route from the previous parts. And it is asking how many times you will be passing through F and H.

So you look at how many edges are connected to the vertices, and since when you go into a point, you always have to also exit the point, that means that any time you pass through the point on your route, you will have to use up two edges. So for every two edges on a vertex there is one visit. So you simply have to count up the edges connecting to a vertex then divide by two.