AlternatingGroupIndex[n, x] gives the cycle index of the alternating group of size n permutations as a polynomial in the symbols x[1], x[2], ..., x[n]}.

AlternatingGroup[n] generates the set of even-size n permutations, the alternating group on n symbols. AlternatingGroup[l] generates the set of even permutations of the list ...

AlternatingPaths[g, start, ME] returns the alternating paths in graph g with respect to the matching ME, starting at the vertices in the list start. The paths are returned in ...

AntiSymmetricQ[g] yields True if the adjacency matrix of g represents an anti-symmetric binary relation.

ArticulationVertices[g] gives a list of all articulation vertices in graph g. These are vertices whose removal will disconnect the graph.

BipartiteMatchingAndCover[g] takes a bipartite graph g and returns a matching with maximum weight along with the dual vertex cover. If the graph is not weighted, it is ...

BipartiteMatching[g] gives the list of edges associated with a maximum matching in bipartite graph g. If the graph is edge weighted, then the function returns a matching with ...

BrelazColoring[g] returns a vertex coloring in which vertices are greedily colored with the smallest available color in decreasing order of vertex degree.

ChromaticPolynomial[g, z] gives the chromatic polynomial P(z) of graph g, which counts the number of ways to color g with, at most, z colors.

CoarserSetPartitionQ[a, b] yields True if set partition b is coarser than set partition a; that is, every block in a is contained in some block in b.