BreadthFirstTraversal[g, v] performs a breadth-first traversal of graph g starting from vertex v, and gives the breadth-first numbers of the vertices. ...

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 ...

CirculantGraph[n, l] constructs a circulant graph on n vertices, meaning the i\[Null]^th vertex is adjacent to the (i + j)\[Null]^th and (i - j)\[Null]^th vertices, for each ...

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 ...

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 ...

KSetPartitions[set, k] returns the list of set partitions of set with k blocks. KSetPartitions[n, k] returns the list of set partitions of {1, 2, ..., n} with k blocks. If ...

PartitionLattice[n] returns a Hasse diagram of the partially ordered set on set partitions of 1 through n in which p < q if q is finer than p, that is, each block in q is ...

SpringEmbedding[g] beautifies the embedding of graph g by modeling the embedding as a system of springs. SpringEmbedding[g, step, increment] can be used to refine the ...

ToOrderedPairs[g] constructs a list of ordered pairs representing the edges of the graph g.

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