 In this video, we provide a solution to question number 11 for practice exam number one for math 1030 Now I do say and a solution because there could actually be more than one There's a lot of different Euler circuits you can construct on this graph now What I'm gonna do is I'm gonna label the edges so we can see what path we're gonna do I'm gonna start right here All of the vertices on this graph are even so the starting point doesn't really matter So I'm gonna do something like this. I'm gonna go up and down So I'm gonna get one and two like so Okay, one and two if you want to kind of draw it. I'm just gonna label them here So I'm gonna go back. So I've gone this so far. I'm gonna go back to my starting point So I'm gonna grab vertex three like so So then I want to kind of my path is I want to go down is I want to go down over here something like that four five six and Seven so again so my path so far as I've snaked around like this So then I can go upwards like this So we could get maybe eight and go down here to be nine So notice what we've done so far Like so What I'm doing is I'm running Fleury's algorithm right now I just make sure you avoid all of the edges that are bridges when they occur bridges and so much that like If you look at the ones you have unvisited those are those would be bridges if you disconnect Once you use them an edge, it's kind of he doesn't exist anymore. So you guys will just remove him from the graph I'm gonna go up here now And then I'm gonna my plans to go up here and maybe kind of come back like this so 10 11 and then 12 Like so so now that we're located here on the graph. We haven't really done anything on the right-hand side So just so you're aware like I basically have used everything on the left-hand side I do have to end up back here when I'm done and my my plan of attack is well Well, I have to use this edge at some point. I haven't used that one yet So that's how I'm gonna get back to the start So at this point I'm gonna try to do as much as I can on the right-hand side The thing is I can't use this edge yet because it's a bridge because there's no way to get away from it So I'm avoiding that one. It's what flurry algorithms does we avoid edges that are bridges and so The next thing that we can do here is we can go maybe up To 13 and then I'm gonna go up here like so so we get like 13 14 and 15 Now that I'm located here. I'm gonna go down like this here here and here like so So 16 17 and 18. I like to do those little caps when I can Now that we're located here, where can we go? We can't go back here yet because that's my only way to get back to the start So I have to avoid that edge for right now, but I could go like up here or I could go over here for the sake of it I'm just gonna go over here. So it'll be 19 That then forces me to go up here. So it's gonna be 20 Now that I'm located here The only place I can go is over here. So it's my only option. So it's gonna be 21 and then from here I gotta go over here. I have no options left 22 is what I'm gonna do there Then you're gonna have to go over here 23 and then you have to go up here to 24 So my options were forced upon me and so now if you check this did this in fact give us another circuit Let's see how we did here 1 to 2 to 3 to 4 to 5 to 6 to 7 to 8 to 9 to 10 to 11 to 12 Then to 13 14 15 16 17 18 19 20 21 22 23 and 24 sure enough This is an oiler circuit every vertex is every edge excuse me is hit once and only once be aware that I did construct this Oiler circuit using flurries algorithm, but flurries are basically to says avoid bridges until you absolutely have to Take them and because of that there are options. There are different Correct answers to this one if you got a different one that doesn't necessarily mean you did this one wrong There are lots of answers as long as you get an oiler circuit I'm perfectly happy with it