graphComplement -- computes the complement of a graph

Synopsis

• Usage:

  L' = graphComplement L

  T = graphComplement S

  H = graphComplement G

• Inputs:

  • L, a list, containing graphs in various formats
  • S, a string, a graph encoded in either Sparse6 or Graph6 format
  • G, an object of class Graph
• Optional inputs:

  • OnlyIfSmaller => a Boolean value, default value false, when true, then the smaller (fewer edges) of the graph and its complement are returned
• Outputs:

  • L', a list, the graph complement of the elements of L stored in Graph6 format
  • T, a string, the graph complement of S stored in the same format at S
  • H, an object of class Graph, the graph complement of G

Description

i1 : graphComplement "Dhc"

o1 = DUW

i2 : graphComplement graph {{1,2},{2,3},{3,4},{4,5},{1,5}}

o2 = Graph{0 => set {2, 3}}
           1 => set {3, 4}
           2 => set {0, 4}
           3 => set {0, 1}
           4 => set {1, 2}

o2 : Graph

i3 : G = generateBipartiteGraphs 7;

i4 : time graphComplement G;
     -- used 0.00131362 seconds

i5 : time (graphComplement \ G);
     -- used 0.161513 seconds