FundamentalCycle takes as input a graph G with a unique cycle and outputs the unique cycle as a graph.  If G has more than one cycle an error is returned.

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

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

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

$C≔\mathrm{FundamentalCycle}\left(G\right)$

$C≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

$\mathrm{Edges}\left(C\right)$

$\left\{\left\{2\,3\right\}\,\left\{2\,5\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\right\}$

$\mathrm{DeleteEdge}\left(G\,\left\{2\,3\right\}\right)$

$\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 5\; edge(s)}$

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

$\mathrm{true}$