  For a formation $\mathfrak{F}$ of finite groups consider a graph whose
vertices are elements of a finite group and two vertices are connected by an
edge if and only if they generates non-$\mathfrak{F}$-group as elements of a
group. A hereditary formation $\mathfrak{F}$ is called regular if the set of
all isolated vertices of the described graph coincides with the intersection of
all maximal $\mathfrak{F}$-subgroups in every group. The constructive
description of saturated regular formations of soluble groups which improves
the results of Lucchini and Nemmi is obtained in this paper. In particular, it
is showed that saturated regular non-empty formations of soluble groups are
just hereditary formations $\mathfrak{F}$ of soluble groups that contains every
group all whose cyclic primary subgroups are $K$-$\mathfrak{F}$-subnormal. Also
we prove that the lattice of saturated regular formations of soluble groups is
lattice isomorphic to the Steinitz's lattice.
