CageGraph[k, r] gives a smallest k-regular graph of girth r for certain small values of k and r. CageGraph[r] gives CageGraph[3, r]. For k = 3, r can be 3, 4, 5, 6, 7, 8, or ...

ChangeEdges[g, e] replaces the edges of graph g with the edges in e. e can have the form {{s_1, t_1}, {s_2, t_2}, ...} or the form {{{s_1, t_1}, gr_1}, {{s_2, t_2}, gr_2}, ...

ChangeVertices[g, v] replaces the vertices of graph g with the vertices in the given list v. v can have the form {{x_1, y_1}, {x_2, y_2}, ...} or the form {{{x_1, y_1}, ...

CompleteGraph[n] creates a complete graph on n vertices. An option Type that takes on the values Directed or Undirected is allowed. The default setting for this option is ...

Dijkstra[g, v] gives a shortest-path spanning tree and associated distances from vertex v of graph g. The shortest-path spanning tree is given by a list in which element i is ...

DominationLattice[n] returns a Hasse diagram of the partially ordered set on integer partitions of n in which p < q if q dominates p. The function takes two options: Type and ...

FromAdjacencyLists[l] constructs an edge list representation for a graph from the given adjacency lists l, using a circular embedding. FromAdjacencyLists[l, v] uses v as the ...

FromUnorderedPairs[l] constructs an edge list representation from a list of unordered pairs l, using a circular embedding.FromUnorderedPairs[l, v] uses v as the embedding for ...

Isomorphism[g, h] gives an isomorphism between graphs g and h if one exists. Isomorphism[g, h, All] gives all isomorphisms between graphs g and h. Isomorphism[g] gives the ...

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 ...