Complete Graph

In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. The complete graph on n vertices has n vertices and n(n-1)/2 edges, and is denoted by K_n. It is a regular graph of degree n-1. All complete graphs are their own cliques. They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. A planar graph cannot contain K_5 (or the complete bipartite graph K_{3,3}) as a minor. Complete graphs on n vertices, for n between 1 and 8, are shown below:

 

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