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.
The object newEdges is a method function.