 In this video we provide the solution to question number two for practice exam number one for math 1030 In which case we're asked given this graph that you see here to the right Which of the following edges is a bridge now there's two ways you could approach this problem We could just go looking for the bridges inside the graph and see See if we can find them all or we can just go pry process of elimination go through these and see which of these are Bridges I'm going to take that second approach here because the graph actually could have more than one bridge In it and this graph definitely has more than six edges So I'm just going to check to see which of these are remember a bridge is an edge Which have removed would disconnect the graph So if we are looking on this graph here look at a x if I remove a x then it turns out the graph is still connected You can reach every other vertex that's still available like in particular you can get anywhere So a x is not the is not the bridge without b y if you remove b y right here Notice how the graph is still connected In particular b can still reach every vertex it could before and so b y is not the edge there That's a bridge if you look at cx something similar is happening if you take out cx You can actually still get from c to x if you detour through b so it's not going to be a bridge B x same thing there if you take away b x you can still get to you from b to x like so And so since there still is a path from b to x that means the graph has to still be connected What about x y here if you take away x y I? Can still get from x to y and therefore since there's still a path from x to y you cannot be a bridge If we're moving an edge if they were to disconnect the graph I mean those two edges and there's no longer a path between them if you can still find a path from the From the two vertices you remove the edge from it means it wasn't a bridge So by process of elimination looks like it's got to be f But let's just check it if you were to remove f Excuse me the answer f which is az if you took away az then aha the vertex z would be isolated from the rest of the graph There is no path between a and z anymore and therefore it turns out f is in fact the correct answer We perhaps could have found that out earlier By looking at the graph but because it turns out that's the only bridge that's on this graph But nonetheless f is the correct answer az is a bridge and the other five are not