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

Synopsis

• Usage:
• Inputs:
• L, a list, containing graphs in various formats
• S, , which describes a graph in Graph6 or Sparse6 format
• G, ,
• Optional inputs:
• MaxDegree => an integer, default value null, the maximum degree allowable for any vertex in the output graphs
• NoNew3Cycles => , default value false, whether graphs with new 3-cycles are allowed
• NoNew4Cycles => , default value false, whether graphs with new 4-cycles are allowed
• NoNew5Cycles => , default value false, whether graphs with new 5-cycles are allowed
• NoNewOddCycles => , 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

Simply creates a list, in the same format as the input, of all possible graphs obtained by adding one new edge to the input graph.

 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

If the List input format is used, then one should use care as the list may contain isomorphic pairs.