neighborhoodComplements -- complements the neighborhood for each vertex, individually

Synopsis

• 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

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

See also

• graphComplement -- computes the complement of a graph
• neighbors -- returns the neighbors of a vertex in a graph