Graph G G is composed of vertices H , I , J , K , L H,I,J,K,L , and edges H I , H J , H K , I K , J K , J L , K L HI,HJ,HK,IK,JK,JL,KL . Which vertices are adjacent to vertex J J ?

Welcome to the practice. In this problem, we have a graph G that is composed of vertices H I J K and L and edges H I H J H K I K J K J L and KL. We'd like to know which vertices are adjacent to vertex J. Now, so far when we've answered these types of questions, we've typically had a picture of a graph and been asked to determine which vertices are adjacent to another vertex. So, one way to answer this question is to actually draw the graph that has these vertices and these edges, and then use it to answer the question. So, let's try doing that method here. Let's start by making our vertices. We have H. I J K and L. And as always, we can arrange these vertices in any way that we'd like, but I just have them generally close together in a circle to make it a bit easier to add in my edges. We have Edges HI. HJ HK I JK JL and KL. Now again, we want to know which vertices are adjacent to vertex J. So, we checked to see which vertices share an edge with vertex J. We can see that there is an edge between J and H, so H is adjacent. There's also an edge between J and K, so K is adjacent, and we have an edge from J to L, so L is also adjacent, and our adjacent vertices are H, K, and L. We don't have an edge from J to I, so they are not adjacent. Now, another way that we could have answered this question is by looking at our edges and seeing which ones include vertex J. Then we take the other vertex in that edge H, K, and L as the three vertices that are adjacent to vertex J. So that's a way to solve the problem if you don't want to draw the graph. I will say you should use whichever method makes it easier for you to answer the question. If you like having the picture, then draw the graph. But if you find it's not too bad to just look through the edges, that will work too. Great job.