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

NumberOfDerangements[n] counts the derangements on n elements, that is, the permutations without any fixed points.

NumberOfKPaths[g, v, k] returns a sorted list that contains the number of paths of length k to different vertices of g from v.NumberOfKPaths[al, v, k] behaves identically, ...

NumberOfNecklaces[n, nc, Cyclic] returns the number of distinct ways in which an n-bead necklace can be colored with nc colors, assuming that two colorings are equivalent if ...

OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...

One is a tag used in several functions to inform the functions that only one object need be considered or only one solution be produced, as opposed to all objects or all ...

Optimum is a value that the option Algorithm can take on when used in functions VertexColoring and VertexCover.

OrbitInventory[ci, x, w] returns the value of the cycle index ci when each formal variable x[i] is replaced by w. OrbitInventory[ci, x, weights] returns the inventory of ...

Ordered is an option to the functions KSubsetGroup and KSubsetGroupIndex that tells the functions whether they should treat the input as sets or tuples.

OrientGraph[g] assigns a direction to each edge of a bridgeless, undirected graph g, so that the graph is strongly connected.