R, a polynomial ring, a ring with exactly two more variables than the ring of G
Outputs:
N', a list, containing graphs in either Graph6 or Sparse6 format, modified as described below
N, a list, a list of graphs, in the same format as the input, modified as described below
Description
The list of "new edge" graphs are formed as follows: Let ab and cd be disjoint edges of G. Then the associated "new edge" graph H is G with the edges ab and cd removed, the vertices e and f added, and the new edges ae, be, cf, df, and ef added.
i1 : R = QQ[a..d];
i2 : G = graph {a*b, c*d};
i3 : S = QQ[a..f];
i4 : newEdges(G, S)
o4 = {Graph{edges => {{a, e}, {b, e}, {c, f}, {d, f}, {e, f}}}}
ring => S
vertices => {a, b, c, d, e, f}
o4 : List
If the List input format is used, then one should use care as the list may contain isomorphic pairs.