CoxeterGraph gives a non-Hamiltonian graph with a high degree of symmetry such that there is a graph automorphism taking any path of length 3 to any other.

CubeConnectedCycle[d] returns the graph obtained by replacing each vertex in a d-dimensional hypercube by a cycle of length d. Cube-connected cycles share many properties ...

DeleteCycle[g, c] deletes a simple cycle c from graph g. c is specified as a sequence of vertices in which the first and last vertices are identical. g can be directed or ...

EdgeColor is an option that allows the user to associate colors with edges. Black is the default color. EdgeColor can be set as part of the graph data structure or in ...

EdgeWeight is an option that allows the user to associate weights with edges. 1 is the default weight. EdgeWeight can be set as part of the graph data structure.

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 ...

NumberOfTableaux[p] uses the hook length formula to count the number of Young tableaux with shape defined by partition p.

PairGroup[g] returns the group induced on 2-sets by the permutation group g. PairGroup[g, Ordered] returns the group induced on ordered pairs with distinct elements by the ...

Partitions[n] constructs all partitions of integer n in reverse lexicographic order. Partitions[n, k] constructs all partitions of the integer n with maximum part at most k, ...

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.