Networks - 2007 VCAA

[Yendall]

The answer here is C:

and

I understand why that is, because they started from a vertex and found the lowest weight (as a guideline, not a rule)
However, A also equals 19 with different weightings. This is how I saw it:

It's fair to say that you should begin from the left and move to the right, but there isn't any real rule when deciding the minimal spanning tree, as long as it's the smallest weight? How can you justify one method as better than the other if you can determine the minimal spanning tree multiple ways? They are assuming that I started from the left and had to pick the smallest weight, however i could've started from the other side and decided 5 + 6 = 11 and 7 + 3 = 10, therefore I chose 7 as the lightest option? And even if that was the case and I have to account for the edge weighted "1", they would still equal 11?

How do I avoid this? How can you determine a correct answer?

[brenden]

If y=7 then that edge wouldn't be included in the minimal spanning tree. If that were the case the total would be 18 because you'd take an edge of 6. We know for a fact that the tree is 19 thus y can't be seven.

[Yendall]

Ah that's so annoying. I'll remember that man thanks!