GraphTheory[SpecialGraphs] - Maple Programming Help

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GraphTheory[SpecialGraphs]

 HigmanSimsGraph
 construct Higman-Sims graph

 Calling Sequence HigmanSimsGraph()

Description

 • The HigmanSimsGraph command creates the Higman-Sims graph, a 22-regular graph with 100 vertices and 1100 edges.
 • The automorphism group of the Higman-Sims graph contains the Higman-Sims group as a subgroup of index 2.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $\mathrm{HS}≔\mathrm{HigmanSimsGraph}\left(\right)$
 ${\mathrm{HS}}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 100 vertices and 1100 edge\left(s\right)}}$ (1)
 > $\mathrm{IsStronglyRegular}\left(\mathrm{HS},'\mathrm{parameters}'\right)$
 ${\mathrm{true}}{,}\left[{22}{,}{0}{,}{6}\right]$ (2)
 > $\mathrm{ChromaticNumber}\left(\mathrm{HS}\right)$
 ${6}$ (3)

References

 "Higman-Sims graph", Wikipedia. http://en.wikipedia.org/wiki/Higman-Sims_graph

Compatibility

 • The GraphTheory[SpecialGraphs][HigmanSimsGraph] command was introduced in Maple 2020.