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complete_graph [2014/02/09 02:40] nikolaj |
complete_graph [2014/02/09 02:42] nikolaj |
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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 === | === Theorems === | ||
| - | A complete graph with $n$ vertices has maximally $\sum_{k=1}^{n-1}k=\frac{1}{2}n(n-1)$ edges. | + | 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]] | ||
