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 ...

ToAdjacencyLists[g] constructs an adjacency list representation for graph g. ToAdjacencyLists[g, EdgeWeight] returns an adjacency list representation along with edge weights.

IndependentEdgeSetQ[g, elist] yields True if the edge list elist is an independent edge set of the graph g, and False otherwise.

AddEdge[g, e] returns a graph g with the new edge e added. e can have the form {a, b} or the form {{a, b}, options}.

EdgeColor is an option that allows the user to associate colors with edges. Black is the default color. EdgeColor can be set as part of the graph data structure or in ...

EdgeLabelColor is an option that allows the user to associate different colors to edge labels. Black is the default color. EdgeLabelColor can be set as part of the graph data ...

EdgeLabelPosition is an option that allows the user to place an edge label in a certain position relative to the midpoint of the edge. LowerLeft is the default value of this ...

EdgeWeight is an option that allows the user to associate weights with edges. 1 is the default weight. EdgeWeight can be set as part of the graph data structure.

EmptyGraph[n] generates an empty graph on n vertices. An option Type that can take on values Directed or Undirected is provided. The default setting is Type -> Undirected.

FranklinGraph returns a 12-vertex graph that represents a 6-chromatic map on the Klein bottle. It is the sole counterexample to Heawood's map-coloring conjecture.