KSubsetGroupIndex[g, s, x] returns the cycle index of the k-subset group on s expressed as a polynomial in x[1], x[2], .... This function also takes the optional argument ...

KSubsets[l, k] gives all subsets of set l containing exactly k elements, ordered lexicographically.

ListGraphs[n, m] returns all nonisomorphic undirected graphs with n vertices and m edges. ListGraphs[n, m, Directed] returns all nonisomorphic directed graphs with n vertices ...

NthPair[n] returns the n\[Null]^th unordered pair of distinct positive integers, when sequenced to minimize the size of the larger integer. Pairs that have the same larger ...

NumberOfKPaths[g, v, k] returns a sorted list that contains the number of paths of length k to different vertices of g from v.NumberOfKPaths[al, v, k] behaves identically, ...

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. ...

Partitions[n] constructs all partitions of integer n in reverse lexicographic order. Partitions[n, k] constructs all partitions of the integer n with maximum part at most k, ...

RadialEmbedding[g, v] constructs a radial embedding of the graph g in which vertices are placed on concentric circles around v depending on their distance from v. ...

RankKSetPartition[sp, s] ranks sp in the list of all k-block set partitions of s. RankSetPartition[sp] ranks sp in the list of all k-block set partitions of the set of ...

SetEdgeLabels[g, l] assigns the labels in l to edges of g.