GeneralizedPetersenGraph[n, k] returns the generalized Petersen graph, for integers n > 1 and k > 0, which is the graph with vertices {u_1, u_2, ..., u_n} and {v_1, v_2, ..., ...

GraphPolynomial[n, x] returns a polynomial in x in which the coefficient of x^m is the number of nonisomorphic graphs with n vertices and m edges. GraphPolynomial[n, x, ...

GridGraph[n, m] constructs an n*m grid graph, the product of paths on n and m vertices. GridGraph[p, q, r] constructs a p*q*r grid graph, the product of GridGraph[p, q] and a ...

IncidenceMatrix[g] returns the (0, 1)-matrix of graph g, which has a row for each vertex and a column for each edge and (v, e) = 1 if and only if vertex v is incident upon ...

KSubsetGroup[pg, s] returns the group induced by a permutation group pg on the set s of k-subsets of [n], where n is the index of pg. The optional argument Type can be ...

ListNecklaces[n, c, Cyclic] returns all distinct necklaces whose beads are colored by colors from c. Here c is a list of n, not necessarily distinct colors, and two colored ...

MakeDirected[g] constructs a directed graph from a given undirected graph g by replacing each undirected edge in g by two directed edges pointing in opposite directions.

NecklacePolynomial[n, c, Cyclic] returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from ...

NumberOfNecklaces[n, nc, Cyclic] returns the number of distinct ways in which an n-bead necklace can be colored with nc colors, assuming that two colorings are equivalent if ...

OrbitInventory[ci, x, w] returns the value of the cycle index ci when each formal variable x[i] is replaced by w. OrbitInventory[ci, x, weights] returns the inventory of ...