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Nauty :: newEdges

newEdges -- replaces disjoint pairs of edges by disjoint pairs of two-chains



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.

Ways to use newEdges :

For the programmer

The object newEdges is a method function.