 In this video, we provide the solution to question number six for practice exam number one for math 1030 In which case we're given a graph like so And we're asked which of the following is an Euler path on the illustrated graph So we could go through all of these paths one by one by one But for Euler paths, there's one very nice thing that can rule out a lot of possibilities The path has to start at odd vertices notice that G and F both have a degree one So they're odd vertices everyone else two four two Four and two so any Euler path has to start at F or G So I can rule out possibility B and possibility C immediately Because they they don't start at F or G also you can throw out possibility A because it doesn't end at F or G Same thing with C It doesn't end at G or F and then so we've already got it down to 50 50 here E and D So I'm only gonna check those ones looking at D right here So D says go from F to B to A to D to E to B to C to D to G That sure sounds like an oil path to me So it feels like D is the winner right there But if you're not if you're not all convinced you can try the other one see what happens F to B to E To D to C to B to E up you use the same edge twice that doesn't quite work So E doesn't work, which of course we already knew that D did work, but in case you just want to check it That's fine. So the correct answer on this one would be D. That is an Euler path. The other five are not