High Quality Content by WIKIPEDIA articles! In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex of the graph. We say an apex, not the apex because an apex graph may have more than one apex (for example, in the minimal nonplanar graphs K5 or K3,3, every vertex is an apex). This class includes graphs that are themselves planar, in which case again every vertex is an apex. For technical reasons, it also includes the null graph.