The DisjointUnion command returns the disjoint union of the input graphs.

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

$G≔\mathrm{DisjointUnion}\left(\mathrm{CycleGraph}\left(3\right)\,\mathrm{PathGraph}\left(3\right)\right)$

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

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

$\left[''1:1''\,''1:2''\,''1:3''\,''2:1''\,''2:2''\,''2:3''\right]$

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

$\left[2\,2\,2\,1\,2\,1\right]$