Complete graph
Graph in which every two vertices are adjacent / From Wikipedia, the free encyclopedia
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In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).[1]
Complete graph  

Vertices  n 
Edges  $\textstyle {\frac {n(n1)}{2}}$ 
Radius  $\left\{{\begin{array}{ll}0&n\leq 1\\1&{\text{otherwise}}\end{array}}\right.$ 
Diameter  $\left\{{\begin{array}{ll}0&n\leq 1\\1&{\text{otherwise}}\end{array}}\right.$ 
Girth  $\left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.$ 
Automorphisms  n! (S_{n}) 
Chromatic number  n 
Chromatic index 

Spectrum  $\left\{{\begin{array}{lll}\emptyset &n=0\\\left\{0^{1}\right\}&n=1\\\left\{(n1)^{1},1^{n1}\right\}&{\text{otherwise}}\end{array}}\right.$ 
Properties  
Notation  K_{n} 
Table of graphs and parameters 
Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, had already appeared in the 13th century, in the work of Ramon Llull.[2] Such a drawing is sometimes referred to as a mystic rose.[3]
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