divisors n builds the graph of divisors. Vertices are integers from 2 to n. i is connected to j if and only if i divides j.

• raises Invalid_argument

  is n < 2.

de_bruijn n builds the de Bruijn graph of order n. Vertices are bit sequences of length n (encoded as their interpretation as binary integers). The sequence xw is connected to the sequence wy for any bits x and y and any bit sequence w of length n-1.

• raises Invalid_argument

  is n < 1 or n > Sys.word_size-1.

vertex_only n builds a graph with n vertices and no edge.

full n builds a graph with n vertices and all possible edges. The optional argument self indicates if loop edges should be added (default value is true).

cycle n builds a graph that is a cycle with n vertices. Vertices are labelled with 0,1,...,n-1 and there is an edge from vertex i to vertex (i+1) mod n. Vertices are also returned in an array for convenience.

grid n m builds a grid graph with n*m vertices, with edges from vertex (i,j) to vertices (i+1,j) and (i,j+1) (and no wrapping around). Vertex (i,j) is labelled with i*m+j. Vertices are also returned in a n*m matrix for convenience.

kneser n k builds the Kneser graph K(n, k), where vertices correspond to the k-element subsets of a set of n elements, and where two vertices are adjacent if and only if the two corresponding sets are disjoint.

Each vertex is labeled with a n-bit integer with exactly k bits set (bit i indicates the selection of the i-th element).

petersen () builds the Petersen graph, that is isomorphic to the Kneser graph K(5,2).