addEdges -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways

Synopsis

• Usage:

  Ll = addEdges L

  Lg = addEdges G

  Ls = addEdges S

• Inputs:
  • L, a list, containing graphs in various formats
  • S, a string, which describes a graph in Graph6 or Sparse6 format
  • G, an instance of the type Graph
• Optional inputs:
  • MaxDegree => an integer, default value null, the maximum degree allowable for any vertex in the output graphs
  • NoNew3Cycles => a Boolean value, default value false, whether graphs with new 3-cycles are allowed
  • NoNew4Cycles => a Boolean value, default value false, whether graphs with new 4-cycles are allowed
  • NoNew5Cycles => a Boolean value, default value false, whether graphs with new 5-cycles are allowed
  • NoNewOddCycles => a Boolean value, default value false, whether graphs with new odd-cycles are allowed
  • NoNewSmallCycles => an integer, default value null, an upper bound on cycles which are not allowed
• Outputs:
  • Ll, a list, the list of graphs obtained from the graphs in $L$ in Graph6 format
  • Lg, a list, the list of graphs obtained from $G$
  • Ls, a list, the list of strings (in Graph6 format) obtained from $S$

Description

i1 : G = graph {{1,2},{2,3},{3,4},{4,5},{1,5}};

i2 : addEdges G

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

o2 : List

See also

• removeEdges -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways