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Nauty :: generateBipartiteGraphs

generateBipartiteGraphs -- generates the bipartite graphs with a given bipartition

Synopsis

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

See also

Ways to use generateBipartiteGraphs :