Maths MEI D1 2006 January paper Question 3

You can find the question here: http://www.mei.org.uk/files/papers/d106ja_lmxhfg.pdf

Question 3 (i) has left me so confused, i have no idea what it is trying to get me to do and the answers aren't helpful in getting me to actually understand the thought process.

Any help?
Thanks.

These sorts of questions often require you to consider the order of each node.

Imagine you want to pass through a node without repeating an edge. When you "enter" the node you use one edge up. When you leave it you use another up. If a node has odd order then eventually there will be one and only one remaining edge which is unused. This means that the node can either be entered, or left, but not both. Thus stopping you starting somewhere, visiting every node and using every edge, and returning to that same node.

This graph is a special graph as it is a digraph. Our start node will be one which we leave once more than we enter, so it is in this case D as that has 2 outs and 1 in. Our end node will be the one which we enter once more than we leave. So in this case that is A.

Wow, thanks for the detailed explanation, it really helped. So basically you are looking for a starting node that allows you to use up all the edges and lands you in a different node at the end.

When finding the start and end node?

yup, am i wrong???