Eulerian[n, k] gives the number of permutations of length n with k runs.
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.
FindSet
(Combinatorica Package Symbol) FindSet[n, s] gives the root of the set containing n in union-find data structure s.
FiniteGraphs produces a convenient list of all the interesting, finite, parameterless graphs built into Combinatorica.
FolkmanGraph returns a smallest graph that is edge-transitive but not vertex-transitive.
FruchtGraph returns the smallest 3-regular graph whose automorphism group consists of only the identity.
GraphCenter[g] gives a list of the vertices of graph g with minimum eccentricity.
GraphDifference[g, h] constructs the graph resulting from subtracting the edges of graph h from the edges of graph g.