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Nauty :: neighborhoodComplements

neighborhoodComplements -- complements the neighborhood for each vertex, individually

Synopsis

Description

The method creates a list of graphs, one for each vertex of the original graph $G$. The graph associated to a vertex $v$ of $G$ has the neighborhood of $v$ complemented.

The method does not remove isomorphs.

i1 : R = QQ[a..e];
i2 : neighborhoodComplements graph {a*b, a*c, b*c, c*d, d*e}

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

o2 : List

See also

Ways to use neighborhoodComplements :

For the programmer

The object neighborhoodComplements is a method function.