The AddVertex command adds a vertex or vertices to a graph. A new graph is returned which contains the specified set of vertices in addition to the vertices in the original graph G.

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

$G≔\mathrm{CycleGraph}\left(5\right)$

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

$\mathrm{AddVertex}\left(G\,\left[''a''\,''b''\right]\right)$

$\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 7\; vertices\; and\; 5\; edge(s)}$

$\mathrm{AddVertex}\left(G\,4\right)$

Error, (in GraphTheory:-AddVertex) some of the vertices to be added are already present in the graph