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 ...

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 ...

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.

Orbits[pg, x] returns the orbits of x induced by the action of the group pg on x.

RandomGraph[n, p] constructs a random labeled graph on n vertices with an edge probability of p.

ShortestPath[g, start, end] finds a shortest path between vertices start and end in graph g.

ShuffleExchangeGraph[n] returns the n-dimensional shuffle-exchange graph whose vertices are length n binary strings with an edge from w to Derivative[1][w] if (i) ...

ToCanonicalSetPartition[sp, set] reorders sp into a canonical order with respect to set. ToCanonicalSetPartition[sp] reorders sp into canonical order, assuming that ...

ToUnorderedPairs[g] constructs a list of unordered pairs representing the edges of graph g. Each edge, directed or undirected, results in a pair in which the smaller vertex ...

VertexCover[g] returns a vertex cover of the graph g.