The IsForest command returns true if the input graph is a forest or false otherwise. A forest is a graph whose connected components are all trees.

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

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

$F≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 3\; edge(s)}$

$\mathrm{IsForest}\left(F\right)$

$\mathrm{true}$

$C≔\mathrm{ConnectedComponents}\left(F\right)$

$C≔\left[\left[1\,2\,3\right]\,\left[4\right]\,\left[5\,6\right]\right]$

$\mathrm{seq}\left(\mathrm{IsTree}\left(\mathrm{InducedSubgraph}\left(F\,i\right)\right)\,i=C\right)$

$\mathrm{true},\mathrm{true},\mathrm{true}$

$\mathrm{NumberOfVertices}\left(F\right)-\mathrm{NumberOfEdges}\left(F\right)-\mathrm{nops}\left(\mathrm{ConnectedComponents}\left(F\right)\right)$

$0$