next | previous | forward | backward | up | index | toc

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

Synopsis

• Usage:
N' = newEdges L
N = newEdges S
N = newEdges G
• Inputs:
• L, a list, containing graphs in various formats
• S, , a graph encoded in either Sparse6 or Graph6 format
• 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 : newEdges graph {{a,b},{c,d}} o1 = {Graph{0 => {4} }} 1 => {4} 2 => {5} 3 => {5} 4 => {0, 1, 5} 5 => {4, 2, 3} o1 : List

If the List input format is used, then one should use care as the list may contain isomorphic pairs.

Ways to use newEdges :

• newEdges(Graph)
• newEdges(List)
• newEdges(String)

For the programmer

The object newEdges is .