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)
G = generateBipartiteGraphs R
G = generateBipartiteGraphs(R, m)
G = generateBipartiteGraphs(R, m, e)
G = generateBipartiteGraphs(R, m, le, ue)
Inputs:
- R, a polynomial ring, the ring in which the graphs will be created
- n, an integer, the number of vertices of the graphs
- m, an integer, the number of vertices in the first part 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 0, an upper bound on the number of common neighbors of vertices in the second class (ignored if zero)
- MaxDegree => an integer, default value 0, an upper bound on the degrees of the vertices (ignored if zero)
- MinDegree => an integer, default value 0, 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

This method generates all bipartite graphs on n vertices. The The size of the bipartition is specified by giving the size of one part; the other part is determined automatically from the number of vertices.

If a PolynomialRing R is supplied instead, then the number of vertices is the number of generators. Moreover, the Strings are automatically converted to graphs in R.

i1 : R = QQ[a..e];

i2 : generateBipartiteGraphs(R, 2)

o2 = {Graph{edges => {}                }, Graph{edges => {{a, e}}          },
            ring => R                           ring => R                    
            vertices => {a, b, c, d, e}         vertices => {a, b, c, d, e}  
     ------------------------------------------------------------------------
     Graph{edges => {{a, e}, {b, e}}  }, Graph{edges => {{a, d}, {a, e}}  },
           ring => R                           ring => R                    
           vertices => {a, b, c, d, e}         vertices => {a, b, c, d, e}  
     ------------------------------------------------------------------------
     Graph{edges => {{a, d}, {b, e}}  }, Graph{edges => {{a, d}, {a, e}, {b,
           ring => R                           ring => R                    
           vertices => {a, b, c, d, e}         vertices => {a, b, c, d, e}  
     ------------------------------------------------------------------------
     e}}}, Graph{edges => {{a, d}, {b, d}, {a, e}, {b, e}}},
                 ring => R                                  
                 vertices => {a, b, c, d, e}                
     ------------------------------------------------------------------------
     Graph{edges => {{a, c}, {a, d}, {a, e}}}, Graph{edges => {{a, c}, {a,
           ring => R                                 ring => R            
           vertices => {a, b, c, d, e}               vertices => {a, b, c,
     ------------------------------------------------------------------------
     d}, {a, e}, {b, e}}}, Graph{edges => {{a, c}, {b, d}, {a, e}}},
                                 ring => R                          
     d, e}                       vertices => {a, b, c, d, e}        
     ------------------------------------------------------------------------
     Graph{edges => {{a, c}, {b, d}, {a, e}, {b, e}}},
           ring => R                                  
           vertices => {a, b, c, d, e}                
     ------------------------------------------------------------------------
     Graph{edges => {{a, c}, {a, d}, {b, d}, {a, e}, {b, e}}},
           ring => R                                          
           vertices => {a, b, c, d, e}                        
     ------------------------------------------------------------------------
     Graph{edges => {{a, c}, {b, c}, {a, d}, {b, d}, {a, e}, {b, e}}}}
           ring => R
           vertices => {a, b, c, d, e}

o2 : List

Ways to use `generateBipartiteGraphs` :

generateBipartiteGraphs(PolynomialRing)
generateBipartiteGraphs(PolynomialRing,ZZ)
generateBipartiteGraphs(PolynomialRing,ZZ,ZZ)
generateBipartiteGraphs(PolynomialRing,ZZ,ZZ,ZZ)
generateBipartiteGraphs(ZZ)
generateBipartiteGraphs(ZZ,ZZ)
generateBipartiteGraphs(ZZ,ZZ,ZZ)
generateBipartiteGraphs(ZZ,ZZ,ZZ,ZZ)

generateBipartiteGraphs -- generates the bipartite graphs with a given bipartition

Synopsis

Description

See also

Ways to use generateBipartiteGraphs :

Ways to use `generateBipartiteGraphs` :