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

DegreesOf2Neighborhood[g, v] returns the sorted list of degrees of vertices of graph g within a distance of 2 from v.

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

ExactRandomGraph[n, e] constructs a random labeled graph of exactly e edges and n vertices.

ExtractCycles[g] gives a maximal list of edge-disjoint cycles in graph g.

FerrersDiagram[p] draws a Ferrers diagram of integer partition p.

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

GraphCenter[g] gives a list of the vertices of graph g with minimum eccentricity.

GrayCodeSubsets[l] constructs a binary reflected Gray code on set l.

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