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Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
complete_graph [2014/02/08 12:55] nikolaj |
complete_graph [2014/02/09 02:40] nikolaj |
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| @#FFBB00: $ \langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ | | | @#FFBB00: $ \langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ | | ||
- | | @#55EE55: $ \langle V,E,\psi\rangle $ ... undirected graph | | + | | @#55EE55: $ \langle V,E,\psi\rangle $ ... simple graph | |
| @#FFFDDD: $ u,v \in V$ | | | @#FFFDDD: $ u,v \in V$ | | ||
- | | @#55EE55: $\{u,u\} $ ... not edge | | ||
| @#55EE55: $ u\neq v\implies \exists !(e\in E).\ \psi(e)=\{u,v\} $ | | | @#55EE55: $ u\neq v\implies \exists !(e\in E).\ \psi(e)=\{u,v\} $ | | ||
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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 === | ||
+ | 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]] | ||
==== Parents ==== | ==== Parents ==== | ||
=== Subset of === | === Subset of === | ||
- | [[Undirected graph]] | + | [[Simple graph]] |