The ShrikhandeGraph command creates the shrikhande graph on 16 vertices. The shrikhande graph is a non-planar 6-regular graph with chromatic number 4 and clique number 3. As an option, you may input the labels of the vertices as a set or list of size 16.

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

$G≔\mathrm{ShrikhandeGraph}\left(\right)\:$

$\mathrm{ChromaticNumber}\left(G\,'c'\right)$

$4$

$c$

$\left[\left[1\,2\,5\,6\right]\,\left[4\,7\,9\,14\right]\,\left[3\,8\,10\,13\right]\,\left[11\,12\,15\,16\right]\right]$

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

$\mathrm{false}$

$\mathrm{IsStronglyRegular}\left(G\,'\mathrm{parameters}'\right)$

$\mathrm{true},\left[6\,2\,2\right]$