SeidelSwitch - Maple Help

GraphTheory

 SeidelSwitch
 construct Seidel switch graph from graph

 Calling Sequence SeidelSwitch(G, S, opts)

Parameters

 G - undirected and unweighted graph S - list of vertices of the graph opts - one or more options as specified below

Options

 • 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.

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{CycleGraph}\left(5\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 5 vertices and 5 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{Neighbors}\left(G,1\right)$
 $\left[{2}{,}{5}\right]$ (2)
 > $H≔\mathrm{SeidelSwitch}\left(G,\left[1,2\right],\mathrm{inplace}=\mathrm{false}\right)$
 ${H}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 5 vertices and 7 edge\left(s\right)}}$ (3)
 > $\mathrm{Neighbors}\left(H,1\right)$
 $\left[{2}{,}{3}{,}{4}\right]$ (4)

Vertices 1 and 2 remain neighbors of each other

 > $\mathrm{DrawGraph}\left(H\right)$
 > $\mathrm{Edges}\left(H\right)$
 $\left\{\left\{{1}{,}{2}\right\}{,}\left\{{1}{,}{3}\right\}{,}\left\{{1}{,}{4}\right\}{,}\left\{{2}{,}{4}\right\}{,}\left\{{2}{,}{5}\right\}{,}\left\{{3}{,}{4}\right\}{,}\left\{{4}{,}{5}\right\}\right\}$ (5)
 > $\mathrm{SeidelSwitch}\left(G,\left[1,2\right]\right)$
 ${\mathrm{Graph 1: an undirected unweighted graph with 5 vertices and 7 edge\left(s\right)}}$ (6)
 > $\mathrm{Edges}\left(G\right)$
 $\left\{\left\{{1}{,}{2}\right\}{,}\left\{{1}{,}{3}\right\}{,}\left\{{1}{,}{4}\right\}{,}\left\{{2}{,}{4}\right\}{,}\left\{{2}{,}{5}\right\}{,}\left\{{3}{,}{4}\right\}{,}\left\{{4}{,}{5}\right\}\right\}$ (7)