An undirected graph G on $n$ vertices is a tree if it is connected and has exactly $n-1$ edges.

The IsTree command returns true if the input graph is a tree, and false otherwise.

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

$T≔\mathrm{Graph}\left(\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\right\}\right)$

$T≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 2\; edges}$

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

$\mathrm{true}$

$C≔\mathrm{Graph}\left(\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{2\,3\right\}\right\}\right)$

$C≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 3\; edges}$

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

$\mathrm{false}$