Transcript for:
Exploring Open and Closed Walks in Graphs

so this video we're going to talk about open and closed walks now this video is going to be really really straightforward and easy but it's important to get it clear in your head because and there's going to be another video about something called trails and another video about something called paths and we need to make sure that we understand what each one is and the subtle differences between them so walks are the easiest and it's a very simple idea here are our towns town a B C D and E and a person is going to walk from town to town to town now the walk that they might do is from A to B from the C from C to e okay and that might be where they finish so if you want to write that walk down you can write it down like this a b c e and that is our walk now it's a bit strange this guy is left town a he's walked through B through C and through e we call this an open walk open walk sorry about squeaking and it's called an open walk because it starts and ends at different vertices okay so you can probably imagine what a closed walk is so a closed walk will start and end at the same vertex so obviously I can close this walk-up by moving from E to 8 and now that is a classic example of a closed walk let's put the example in there A to B to C to E and back to a now I should put some arrows in to show the direction that my Walker is walking in okay now I just want to go through some other open and closed walks because a walk can really look like a lot of different things you can do whatever you want when it comes to walks all right so I've cleaned up my network let's go for another walk we might start at D and then we might move from E to C and then I'm going to go from C back to D and then I'm going to go through this loop and then I'm going to go back to C because I enjoyed it so much and then I'm going to go from C to B okay that's enough let's write that walk down so I started at D I went to E then I went to C then I went back to D then I did the loop which means I went back to D and then I went back to C and then I went to be and I'm finished now at the moment that is an open walk because it starts and ends at different vertices but the thing that I want you to see here is two things I went to the same vertex a number of times I went to D I started at D and I went back to D twice I went to see twice so a walk can visit a town multiple times the other thing I want you to see here is that roads or edges were visited multiple times as well I walked along that road twice okay so in a walk anything goes you can walk to multi you can walk to the same town multiple times you can walk along the same edge multiple times now we're going to talk about paths and trails coming up and those we're going to put some restrictions on that when it comes to paths and trails but with a walk anything goes at the moment that's an open walk and I might just close the walk up to finish that video so he goes from A to E back to D and he's very easy to tell if a walk is closed or not just look at the first and last letters if the first and last letters are the same then it must be a closed walk all right those are open and closed walks