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.