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 : R = QQ[a..e];

i2 : graphComplement cycle R

o2 = Graph{edges => {{a, c}, {a, d}, {b, d}, {b, e}, {c, e}}}
           ring => R
           vertices => {a, b, c, d, e}

o2 : Graph

i3 : graphComplement "Dhc"

o3 = DUW

i4 : G = generateBipartiteGraphs 7;

i5 : time graphComplement G;
     -- used 0.00122794 seconds

i6 : time (graphComplement \ G);
     -- used 0.152697 seconds

See also

• complementGraph -- returns the complement of a graph or hypergraph