SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

ToCycles[p] gives the cycle structure of permutation p as a list of cyclic permutations.

TopologicalSort[g] gives a permutation of the vertices of the directed acyclic graph g such that an edge (i, j) implies that vertex i appears before vertex j.

TransitiveClosure[g] finds the transitive closure of graph g, the supergraph of g that contains edge {x, y} if and only if there is a path from x to y.

VertexConnectivityGraph[g] returns a directed graph that contains an edge corresponding to each vertex in g and in which edge-disjoint paths correspond to vertex-disjoint ...

VertexConnectivity[g] gives the minimum number of vertices whose deletion from graph g disconnects it. VertexConnectivity[g, Cut] gives a set of vertices of minimum size ...

VertexStyle is an option that allows the user to associate different sizes and shapes to vertices.

Vertices[g] gives the coordinates of each vertex of graph g embedded in a plane.Vertices[g, All] gives the embedding of the graph along with graphics options associated with ...

Wheel[n] constructs a wheel on n vertices, which is the join of CompleteGraph[1] and Cycle[n - 1].

Zoom[{i, j, k, ...}] is a value that the PlotRange option can take on in ShowGraph. Setting PlotRange to this value zooms the display to contain the specified subset of ...