PartialOrderQ[g] yields True if the binary relation defined by edges of the graph g is a partial order, meaning it is transitive, reflexive, and antisymmetric. ...

PartitionQ[p] yields True if p is an integer partition. PartitionQ[n, p] yields True if p is a partition of n.

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.

RandomSubset[l] creates a random subset of set l.

SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

SymmetricQ[r] tests if a given square matrix r represents a symmetric relation. SymmetricQ[g] tests if the edges of a given graph represent a symmetric relation.

TransposePartition[p] reflects a partition p of k parts along the main diagonal, creating a partition with maximum part k.

VertexColor is an option that allows the user to associate colors with vertices.

VertexLabelColor is an option that allows the user to associate different colors to vertex labels.

VertexLabel is an option that can take on values True or False, allowing the user to set and display vertex labels.