# 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 graph encoded in either Sparse6 or Graph6 format
• G, ,
• 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