In this course, we will study mathematical objects called graphs . This kind of graph can be precisely defined to be a set of ordered pairs. The pictorial representations of the cube and octahedral graphs show how they got their names - both can be drawn so that they resemble a drawing of a cube or an octahedron. Graphs from an Abstract Viewpoint Pictures of graphs showing all of the edges and vertices are great ways to represent a graph. It is immediately clear which vertices are joined by edges, and you can often recognize the graph from its picture.
Every vertex meets exactly three vertices.
If you see a picture that looks exactly like a cube, then you know immediately that you are dealing with the cube graph. However, pictorial representations of graphs have their limitations, too. For example, if you wanted to prove a theorem about graphs, and all you had were pictorial representations, then your proof might have to consist of drawing every single, possible graph, and then demonstrating the truth of your theorem for each picture that you have drawn. A pretty time-consuming process, to say the least. G consists of a set of vertices and a set of edges, where each edge joins an unordered pair of vertices.