SeidelSpectrum - Maple Help

GraphTheory

 SeidelSpectrum
 compute Seidel spectrum

 Calling Sequence SeidelSpectrum(G)

Parameters

 G - graph

Description

 • The SeidelSpectrum command returns the Seidel spectrum of the eigenvalues of a specified graph. That is the set of eigenvalues of the matrix $J-I-2A$ where $J$ is the all-one matrix, $I$ is the identity matrix and $A$ is the adjacency matrix of the graph. The output is a list $L$. Each element of $L$ is a list of size 2, where the first element is an eigenvalue and the second element is its multiplicity.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $G≔\mathrm{ClebschGraph}\left(\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 16 vertices and 40 edge\left(s\right)}}$ (1)
 > $\mathrm{SeidelSpectrum}\left(G\right)$
 $\left[\left[{-3}{,}{10}\right]{,}\left[{5}{,}{6}\right]\right]$ (2)
 > $P≔\mathrm{PetersenGraph}\left(\right)$
 ${P}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 10 vertices and 15 edge\left(s\right)}}$ (3)
 > $\mathrm{SeidelSpectrum}\left(P\right)$
 $\left[\left[{-3}{,}{5}\right]{,}\left[{3}{,}{5}\right]\right]$ (4)