ChvatalGraph returns a smallest triangle-free, 4-regular, 4-chromatic graph.

CubicalGraph returns the graph corresponding to the cube, a Platonic solid.

DodecahedralGraph returns the graph corresponding to the dodecahedron, a Platonic solid.

FolkmanGraph returns a smallest graph that is edge-transitive but not vertex-transitive.

FruchtGraph returns the smallest 3-regular graph whose automorphism group consists of only the identity.

GrayGraph returns a 3-regular, 54-vertex graph that is edge-transitive but not vertex-transitive\[LongDash]the smallest known such example.

GroetzschGraph returns the smallest triangle-free graph with chromatic number 4. This is identical to MycielskiGraph[4].

HeawoodGraph returns a smallest (6, 3)-cage, a 3-regular graph with girth 6.

HerschelGraph returns a graph object that represents a Herschel graph.

Hypercube[n] constructs an n-dimensional hypercube.