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Complete graph
Set
$V,E$ … set |
$ \langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ |
$ \langle V,E,\psi\rangle $ … simple graph |
$ u,v \in V$ |
$ u\neq v\implies \exists !(e\in E).\ \psi(e)=\{u,v\} $ |
Discussion
In a complete (undirected) graph, every two distinct vertices are connected.
The axiom $\{u\}\notin\mathrm{im}(\psi)$ says that there are no loops on a single vertex.
Theorems
A complete graph with $n$ vertices has maximally $\sum_{k=1}^{n-1}k=\frac{1}{2}n(n-1)$ edges.
Reference
Wikipedia: Complete graph