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.

IcosahedralGraph returns the graph corresponding to the icosahedron, a Platonic solid.

LeviGraph returns the unique (8, 3)-cage, a 3-regular graph whose girth is 8.

McGeeGraph returns the unique (7, 3)-cage, a 3-regular graph with girth 7.

MycielskiGraph[k] returns a triangle-free graph with chromatic number k, for any positive integer k.