Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
complete_graph [2014/02/08 14:14]
nikolaj
complete_graph [2014/03/21 11:11] (current)
Line 1: Line 1:
 ===== Complete graph ===== ===== Complete graph =====
 ==== Set ==== ==== Set ====
-| @#88DDEE: $V,E$ ... set |+| @#55CCEE: context ​    | @#55CCEE: $V,E$ ... set |
  
-| @#FFBB00: $ \langle V,​E,​\psi\rangle \in \mathrm{it}(E,​V) $ |+| @#FFBB00: definiendum ​| @#FFBB00: $ \langle V,​E,​\psi\rangle \in \mathrm{it}(E,​V) $ |
  
-| @#55EE55: $ \langle V,​E,​\psi\rangle $ ... simple graph |+| @#55EE55: postulate ​  | @#55EE55: $ \langle V,​E,​\psi\rangle $ ... simple graph |
  
-| @#FFFDDD: $ u,v \in V$ |+| @#FFFDDD: for all     | @#FFFDDD: $ u,v \in V$ |
  
-| @#55EE55: $ u\neq v\implies \exists !(e\in E).\ \psi(e)=\{u,​v\} $ |+| @#55EE55: postulate ​  | @#55EE55: $ u\neq v\implies \exists !(e\in E).\ \psi(e)=\{u,​v\} $ |
  
 ==== Discussion ==== ==== Discussion ====
Line 15: Line 15:
  
 The axiom $\{u\}\notin\mathrm{im}(\psi)$ says that there are no loops on a single vertex. The axiom $\{u\}\notin\mathrm{im}(\psi)$ says that there are no loops on a single vertex.
 +=== Theorems ===
 +When dealing with simple graphs, if you add another vertex to a graph with $n$ vertices, you can add $n$ new edges at best. So a complete graph with $n$ vertices has maximally $\sum_{k=1}^{n-1}k=\frac{1}{2}n(n-1)$ edges.
 === Reference === === Reference ===
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Complete_graph|Complete graph]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Complete_graph|Complete graph]]
Link to graph
Log In
Improvements of the human condition