InversionPoset[n] returns a Hasse diagram of the partially ordered set on size-n permutations in which p < q if q can be obtained from p by an adjacent transposition that ...

IsomorphicQ[g, h] yields True if graphs g and h are isomorphic.

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 ...

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.

ShortestPathSpanningTree[g, v] constructs a shortest-path spanning tree rooted at v, so that a shortest path in graph g from v to any other vertex is a path in the tree.

ToAdjacencyLists[g] constructs an adjacency list representation for graph g. ToAdjacencyLists[g, EdgeWeight] returns an adjacency list representation along with edge weights.

ToAdjacencyMatrix[g] constructs an adjacency matrix representation for graph g. ToAdjacencyMatrix[g, EdgeWeight] returns edge weights as entries of the adjacency matrix with ...

VertexColoring[g] uses Brelaz's heuristic to find a good, but not necessarily minimal, vertex coloring of graph g.

New functions SymmetricPolynomial and SymmetricReduction have been added to the built-in Mathematica kernel.