CycleIndex[pg, x] returns the polynomial in x[1], x[2], ..., x[index[pg]] that is the cycle index of the permutation group pg. Here index[pg] refers to the length of each ...

Eccentricity[g] gives the eccentricity of each vertex v of graph g, the maximum length among all shortest paths from v.

EdgeChromaticNumber[g] gives the fewest number of colors necessary to color each edge of graph g, so that no two edges incident on the same vertex have the same color.

GraphJoin[g_1, g_2, ...] constructs the join of graphs g_1, g_2, and so on. This is the graph obtained by adding all possible edges between different graphs to the graph ...

GraphUnion[g_1, g_2, ...] constructs the union of graphs g_1, g_2, and so forth. GraphUnion[n, g] constructs n copies of graph g, for any nonnegative integer n.

Index[p] gives the index of permutation p, the sum of all subscripts j such that p[[j]] is greater than p[[j + 1]].

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

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

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 ...