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, a 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, a 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 => {2, 3}}
           1 => {3, 4}
           2 => {0, 4}
           3 => {0, 1}
           4 => {2, 1}

o2 : Graph

i3 : G = generateBipartiteGraphs 7;

i4 : time graphComplement G;
     -- used 0.000344852 seconds

i5 : time (graphComplement \ G);
     -- used 0.126895 seconds