  Given a formation $\mathfrak F$, we consider the graph whose vertices are the
elements of $G$ and where two vertices $g,h\in G$ are adjacent if and only if
$\langle g,h \rangle \notin\mathfrak F$. We are interested in the two following
questions. Is the set of the isolated vertices of this graph a subgroup of $G$?
Is the subgraph obtained by deleting the isolated vertices a connected graph?
