RelabelVertices(G,V) returns a new graph with vertex labels changed to be those in V.  The graph G is not modified.

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

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

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

$\left[1\,2\,3\,4\right]$

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

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\right\}$

$H≔\mathrm{RelabelVertices}\left(G\,\left[a\,b\,c\,d\right]\right)\:$

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

$\left[a\,b\,c\,d\right]$

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

$\left\{\left\{a\,b\right\}\,\left\{a\,c\right\}\,\left\{a\,d\right\}\right\}$