# removeEdges -- creates a list of graphs obtained by removing one edge from the given graph in all possible ways

## Synopsis

• Usage:
R' = removeEdges L
R = removeEdges S
R = removeEdges G
• Inputs:
• L, a list, containing graphs in various formats
• S, , a graph encoded in either Sparse6 or Graph6 format
• G, ,
• Optional inputs:
• MinDegree => an integer, default value null, the minimum degree which a returned graph can have
• Outputs:
• R', a list, a list of all graphs obtained by removed one edge from the given graphs; it contains graphs in Graph6 or Sparse6 format
• R, a list, a list of all graphs obtained by removed one edge from the given graph; it contains graphs in the same format as the input

## Description

This method creates a list of all possible graphs obtainable from the given graph by removing one edge. Notice that isomorphic graphs are allowed within the list.

 i1 : R = QQ[a..e]; i2 : removeEdges cycle R o2 = {Graph{edges => {{b, c}, {c, d}, {a, e}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {b, c}, {c, d}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {c, d}, {a, e}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {b, c}, {a, e}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {b, c}, {c, d}, {a, e}}}} ring => R vertices => {a, b, c, d, e} o2 : List i3 : removeEdges graph {a*b, a*c, b*c, c*d, d*e} o3 = {Graph{edges => {{a, c}, {b, c}, {c, d}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {b, c}, {c, d}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {a, c}, {c, d}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {a, c}, {b, c}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {a, c}, {b, c}, {c, d}}}} ring => R vertices => {a, b, c, d, e} o3 : List

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

## See also

• addEdges -- creates a list of graphs obtained by adding one new edge to the given graph in all possible ways

## Ways to use removeEdges :

• "removeEdges(Graph)"
• "removeEdges(List)"
• "removeEdges(String)"

## For the programmer

The object removeEdges is .