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, a 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 : R = QQ[a..e];

i2 : addEdges cycle R

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

o2 : List

See also

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