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

• Usage:

  G = generateGraphs n

  G = generateGraphs(n, e)

  G = generateGraphs(n, le, ue)

• Inputs:
  • n, an integer, the number of vertices of the graphs, must be positive (see caveat)
  • 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:
  • 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
  • Only4CycleFree => a Boolean value, default value false, whether to only allow graphs without 4-cycles
  • OnlyBiconnected => a Boolean value, default value false, whether to only allow biconnected graphs
  • OnlyBipartite => a Boolean value, default value false, whether to only allow bipartite graphs
  • OnlyConnected => a Boolean value, default value false, whether to only allow connected graphs
  • OnlyTriangleFree => a Boolean value, default value false, whether to only allow graphs without triangles (3-cycles)
• Outputs:
  • G, a list, the graphs satisfying the input conditions

i1 : generateGraphs(5, 4, 6, OnlyConnected => true)

o1 = {D?{, DCw, DC{, DEw, DEk, DE{, DFw, DQo, DQw, DQ{, DUW, DUw, DTw}

o1 : List