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.
newEdges graph {{a,b},{c,d}} |
If the List input format is used, then one should use care as the list may contain isomorphic pairs.