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 ...

LexicographicSubsets[l] gives all subsets of set l in lexicographic order. LexicographicSubsets[n] returns all subsets of {1, 2, ..., n} in lexicographic order.

Neighborhood[g, v, k] returns the subset of vertices in g that are at a distance of k or less from vertex v. Neighborhood[al, v, k] behaves identically, except that it takes ...

NextBinarySubset[l, s] constructs the subset of l following subset s in the order obtained by interpreting subsets as binary string representations of integers.

NormalizeVertices[v] gives a list of vertices with a similar embedding as v but with the coordinates of all points scaled to be between 0 and 1.

NumberOfDirectedGraphs[n] returns the number of nonisomorphic directed graphs with n vertices. NumberOfDirectedGraphs[n, m] returns the number of nonisomorphic directed ...

NumberOfGraphs[n] returns the number of nonisomorphic undirected graphs with n vertices. NumberOfGraphs[n, m] returns the number of nonisomorphic undirected graphs with n ...

OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...

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, ...

PerfectQ[g] yields True if g is a perfect graph, meaning that for every induced subgraph of g the size of a largest clique equals the chromatic number.