DeleteVertex[g, v] deletes a single vertex v from graph g. Here v is a vertex number.

Eulerian[n, k] gives the number of permutations of length n with k runs.

GroetzschGraph returns the smallest triangle-free graph with chromatic number 4. This is identical to MycielskiGraph[4].

Inversions[p] counts the number of inversions in permutation p.

MinimumChainPartition[g] partitions partial-order g into a minimum number of chains.

MycielskiGraph[k] returns a triangle-free graph with chromatic number k, for any positive integer k.

NumberOf2Paths[g, v] returns a sorted list that contains the number of paths of length 2 to different vertices of g from v.

NumberOfCompositions[n, k] counts the number of distinct compositions of integer n into k parts.

NumberOfSpanningTrees[g] gives the number of labeled spanning trees of graph g.

Uniquely3ColorableGraph returns a 12-vertex, triangle-free graph with chromatic number 3 that is uniquely 3-colorable.