inplace=truefalse

Specifies whether the changes are applied to the original graph or to a copy. The default is true, meaning the original graph is changed.

The SeidelSwitch command transforms the input graph to a new graph in such a way that, for each specified vertex, its neighbors become its non-neighbors and vice versa.

By default, the original graph is changed and the switching happens in place. By setting inplace=false the original graph remains unchanged.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$G≔\mathrm{CycleGraph}\left(5\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 5\; edge(s)}$

$\mathrm{DrawGraph}\left(G\right)$

$\mathrm{Neighbors}\left(G\,1\right)$

$\left[2\,5\right]$

$H≔\mathrm{SeidelSwitch}\left(G\,\left[1\,2\right]\,\mathrm{inplace}=\mathrm{false}\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 7\; edge(s)}$

$\mathrm{Neighbors}\left(H\,1\right)$

$\left[2\,3\,4\right]$

$\mathrm{DrawGraph}\left(H\right)$

$\mathrm{Edges}\left(H\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\right\}$

$\mathrm{SeidelSwitch}\left(G\,\left[1\,2\right]\right)$

$\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 7\; edge(s)}$

$\mathrm{Edges}\left(G\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\right\}$