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.

CodeToLabeledTree[l] constructs the unique labeled tree on n vertices from the Prüfer code l, which consists of a list of n - 2 integers between 1 and n.

Cyclic is an argument to the Polya-theoretic functions ListNecklaces, NumberOfNecklaces, and NecklacePolynomial, which count or enumerate distinct necklaces. Cyclic refers to ...

Dihedral is an argument to the Polya-theoretic functions ListNecklaces, NumberOfNecklaces, and NecklacePolynomial, which count or enumerate distinct necklaces. Dihedral ...

KnightsTourGraph[m, n] returns a graph with mn vertices in which each vertex represents a square in an m*n chessboard and each edge corresponds to a legal move by a knight ...

PermutationWithCycle[n, {i, j, ...}] gives a size-n permutation in which {i, j, ...} is a cycle and all other elements are fixed points.

SamenessRelation[l] constructs a binary relation from a list l of permutations, which is an equivalence relation if l is a permutation group.

SetPartitionToRGF[sp, set] converts the set partition sp of set into the corresponding restricted growth function.

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 ...

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