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 valence n-1.
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:
n Kn
n Kn 1 
5 
2 
6 
3 
7 
4
8 