IsCutSet tests whether the edge set E is a cut-set of the graph G. If so, then removing the edges of E disconnects the graph if the graph is connected or, in general, increase the number of connected components.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$G≔\mathrm{Graph}\left(\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{2\,3\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\,\left\{4\,6\right\}\,\left\{5\,6\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 8\; edge(s)}$

$\mathrm{DrawGraph}\left(G\right)$

$S≔\left\{\left\{1\,4\right\}\,\left\{3\,4\right\}\right\}$

$S≔\left\{\left\{1\,4\right\}\,\left\{3\,4\right\}\right\}$

$\mathrm{IsCutSet}\left(G\,S\right)$

$\mathrm{true}$

$\mathrm{DeleteEdge}\left(G\,S\right)$

$\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 6\; edge(s)}$

$\mathrm{IsConnected}\left(G\right)$

$\mathrm{false}$