ChangeVertices[g, v] replaces the vertices of graph g with the vertices in the given list v. v can have the form {{x_1, y_1}, {x_2, y_2}, ...} or the form {{{x_1, y_1}, ...

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 ...

CompleteGraph[n] creates a complete graph on n vertices. An option Type that takes on the values Directed or Undirected is allowed. The default setting for this option is ...

CompleteKPartiteGraph[a, b, c, ...] creates a complete k-partite graph of the prescribed shape, provided the k arguments a, b, c, ... are positive integers. An option Type ...

ConnectedQ[g] yields True if undirected graph g is connected. If g is directed, the function returns True if the underlying undirected graph is connected. ConnectedQ[g, ...

CubeConnectedCycle[d] returns the graph obtained by replacing each vertex in a d-dimensional hypercube by a cycle of length d. Cube-connected cycles share many properties ...

Cycle[n] constructs the cycle on n vertices, the 2-regular connected graph. An option Type that takes on values Directed or Undirected is allowed. The default setting is Type ...

DeBruijnSequence[a, n] returns a De Bruijn sequence on the alphabet a, a shortest sequence in which every string of length n on alphabet a occurs as a contiguous subsequence.

DeleteCycle[g, c] deletes a simple cycle c from graph g. c is specified as a sequence of vertices in which the first and last vertices are identical. g can be directed or ...

DeleteEdge[g, e] gives graph g minus e. If g is undirected, then e is treated as an undirected edge; otherwise it is treated as a directed edge. If there are multiple edges ...