generateBipartiteGraphs -- generates the bipartite graphs with a given bipartition

Synopsis

• Usage:

  G = generateBipartiteGraphs n

  G = generateBipartiteGraphs(n, m)

  G = generateBipartiteGraphs(n, m, e)

  G = generateBipartiteGraphs(n, m, le, ue)

• Inputs:
  • n, an integer, the number of vertices of the graphs, must be positive (see caveat)
  • m, an integer, the number of vertices in the first class of the bipartition
  • e, an integer, the number of edges in the graphs
  • le, an integer, a lower bound on the number of edges in the graphs
  • ue, an integer, an upper bound on the number of edges in the graphs
• Optional inputs:
  • Class2Degree2 => a Boolean value, default value false, whether the vertices in the second class must have at least two neighbors of degree at least 2
  • Class2DistinctNeighborhoods => a Boolean value, default value false, whether all vertices in the second class must have distinct neighborhoods
  • Class2MaxCommonNeighbors => an integer, default value null, an upper bound on the number of common neighbors of vertices in the second class
  • MaxDegree => an integer, default value null, an upper bound on the degrees of the vertices
  • MinDegree => an integer, default value null, a lower bound on the degrees of the vertices
  • OnlyConnected => a Boolean value, default value false, whether to only allow connected graphs
• Outputs:
  • G, a list, the bipartite graphs satisfying the input conditions

Description

Caveat

See also

• generateGraphs -- generates the graphs on a given number of vertices