Complete graph
A complete graph is a simple graph where an edge connects every pair of vertices. A complete graph on n vertices has n vertices and n(n−1)/2 edges, and is indicated by the notation Kn. It is a regular graph of degree n−1. All complete graphs are their own cliques. A planar graph cannot contain K5 (or the complete bipartite graph K3,3).
A complete bipartite graph is a graph with vertices segregated into two sets, where an edge connects every pair of vertices where they are not in the same set.
Complete graphs on n vertices, for n between 1 and 8, are shown below:
