  In this paper we define a way to get a bounded invertible automaton starting
from a finite graph. It turns out that the corresponding automaton group is
regular weakly branch over its commutator subgroup, contains a free semigroup
on two elements and is amenable of exponential growth. We also highlight a
connection between our construction and the right-angled Artin groups. We then
study the Schreier graphs associated with the self-similar action of these
automaton groups on the regular rooted tree. We explicitly determine their
diameter and their automorphism group in the case where the initial graph is a
path. Moreover, we show that the case of cycles gives rise to Schreier graphs
whose automorphism group is isomorphic to the dihedral group. It is remarkable
that our construction recovers some classical examples of automaton groups like
the Adding machine and the Tangled odometer.
