This problem asks us to create graphs that represent flights between cities and then identify what type of graphs those are as a result of how they look. So, um, where I started with this was summarizing the given information, so I just kind of made myself a visual to the side. The way I set this up shows that there's four flights from Boston to New York to flights from New York to Boston and so forth. So there's lots of ways you could do that. But having that kind of summarized out to the side is gonna help me a lot. I also went ahead and already set up. All of my Vergis is. So when you're doing that, something you might want to think about when you're strategizing is thinking about what City has the most connections to the others. In this case, that's Newark. So I kinda situated that in the middle to help me have space. Most of all, a Z. I'm looking to connect those as we go through each part of this. There's subtle differences, and so you wanna be looking for keywords in the problem. Andi, as I went through those I just kind of summarized each also, so hopefully that'll help us as we go. Um, but let's go and start with a For part A. We wanted an edge between cities that have a flight between them in either direction was kind of a keyword there, telling us that direction does not matter on DSO. We want to connect each pair of cities that have flights between them, and this will be really simple. We see that Boston and New York have one on and New York and Miami, American, Detroit, American Washington and then Miami in Washington. So that's all we have to do for that one. As you're looking into the table to help you classify, we can notice that this is an undirected graph. It didn't matter what direction these were going in. It doesn't have multiple edges between Verdecia because we were just looking toe show the pair's and there's no loops. So this is a simple graph moving on to Part B. We want an edge in this case for each flight in either direction. So again, direction is not going to matter. This will be an undirected graph, but this time we want an edge, representing each flight. So each flight is definitely key. Word here, as I'm looking kind of to my summarized information over here, I know that there's going to be six total flights between Boston and Newark, 5 35 and one between each of those pairs of cities. And so I'm just trying to fit in six edges between Boston and work, which might be a tight squeeze. But we're going to do our best. Um, something that you want to keep in mind is your drawing these in, though, is that you do wanna leave space between each of the edges so that you can tell that there are multiple lines there. So that is five total between your work and Detroit's three right American Washington's five, then my me Washington just has one, um, again try to make. This is Nida's you can. But at the end of the day, you need to have the total number of flights between each city that number of artists, there's of edges. Excuse me. So we're looking Thio. Identify this. We have an undirected graph, but this time we have multiple edges between the verdict sees we still don't have any loops. And so this one is called a multi crap multi graph. Mhm. Yeah. So as we go forward curtsy had the exact same scenario is part beaded. Except now we're adding a sightseeing loop around Miami. So I'm just gonna drawing that I had on the last slide a little bit quicker this time. We're trying to you need them. So, six between New York and Boston, you need five here for me. Mind not one. Oops. That one between Miami and Washington Still, But now we're adding in a loop. And, of course, on a graph that just looks like a school. So something like that. Um, So we have the same scenario we're looking to classify again to undirected multiple edges between the verdict sees. But this time we do have loops. And so this one we will classify as a pseudo graph again. I'm using kind of the parameters that are given in that table for each of those so you can look it, um, those help you as you're classifying Part D says, um, in essence, that we need an edge from each origin city to each destination city. Um and so the key here is that direction does matter because it's telling us where we need to start and where we need to finish. Also, it doesn't say that we need one for each flight, though, So that's, um, telling us that we're not needing multiple edges like showing each flight. So as I'm looking to my summarized information, I know that there's flights from Boston to New York, so I need to show that on. We put these arrows in to show the direction, and then there's flights from New York to Boston. Mhm on. But of course there is. In the opposite direction is, um, same thing New York and Miami. They have flights in either direction. Same current Eric in Detroit, American Washington. Try your best to show what? Chinese air pointing also. Mhm. And last but not least, we have this one from Washington to Miami. Okay, you in Alright. So that's representing kind of all of the pairs again of origins and destinations this time. So, as we look to classify, we have directed graph because we included those arrows. Has, um it looks like multiple edges, so don't be tricked here. Um, this doesn't count as multiple edges in the sense of there's not multiple edges going in the same direction. So, um and there's no loops. It's the last thing that we're checking for each of these. So in that sense, this is going to be a simple directed graph again. Even though there's multiple edges between the Vergis sees, they are not in the same direction. So not counting as kind of representing the same thing. Our very last one here is very similar to D, but now we want toe say that there's an edge for each flight. So back Thio needing six between Boston and Newark child using. But the key here now is that the direction does matter. So we need Thio show show which direction each of these air going in. So let us do this for now. I think that's still clear which way that's going. So for pointing this direction to pointing from network from Newark to Boston between New York and Miami, we'll have five total and three air going from New York to Miami. Two are going from Miami to New York. Go back just a second ever believe in, Um and this is the way we're going Thio her scene So New York to Detroit has one Detroit to New York. Cast him New York Washington's 30. So the New York to Washington is three office attractions to and finally from Washington to Miami. Just have one. So as I'm drawing these arrows again, they're pointing in the direction that they're going, so hopefully that's pretty clear. And so, as we're looking to classify this last one, we do have a directed graph. We have multiple edges between the Verte sees in the sense that even multiple and going in the same direction, Um, and that's really the key here. There's no loops, obviously, but that's the defining characteristic is the multiple edges. So this one is going to be called a directed multi gra. You can see where the name came from, directed and multiple edges, and we're all set