neighborhoodComplements -- complements the neighborhood for each vertex, individually

Usage:

N' = neighborhoodComplements L

N = neighborhoodComplements S

N = neighborhoodComplements G
Inputs:
- L, a list, containing graphs in various formats
- S, a string, a graph encoded in either Sparse6 or Graph6 format
- G, a graph,
Outputs:
- N', a list, containing graphs in either Graph6 or Sparse6 format, modified as described below
- N, a list, containing graphs, in the same format as the input, modified as described below

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 : neighborhoodComplements graph {{1,2},{1,3},{2,3},{3,4},{4,5}}

o1 = {Graph{0 => {1, 2}      }, Graph{0 => {1, 2, 3, 4}}, Graph{0 => {1, 2,
            1 => {0, 2, 3, 4}         1 => {0, 2}               1 => {0, 2,
            2 => {1, 0, 4}            2 => {1, 0, 4}            2 => {1, 0,
            3 => {1, 4}               3 => {0, 4}               3 => {2}   
            4 => {1, 2, 3}            4 => {0, 2, 3}            4 => {1, 0}
     ------------------------------------------------------------------------
     4}}, Graph{0 => {1, 4}   }, Graph{0 => {1, 2, 3}}}
     4}         1 => {0, 4}            1 => {0, 2, 3}
     3}         2 => {3}               2 => {1, 0}
                3 => {2, 4}            3 => {1, 0, 4}
                4 => {1, 0, 3}         4 => {3}

o1 : List

Ways to use neighborhoodComplements:

neighborhoodComplements(Graph)
neighborhoodComplements(List)
neighborhoodComplements(String)

For the programmer

The object neighborhoodComplements is a method function.

The source of this document is in NautyGraphs.m2:1306:0.

neighborhoodComplements -- complements the neighborhood for each vertex, individually

Description

See also

Ways to use neighborhoodComplements:

For the programmer