The current study aims to establish a connection between graphs and automata theory, which apparently demonstrate di erent mathematical structures. Through searching out some properties of one of these structures, we try to  nd some new properties of the other structure as well. This will result in obtaining some unknown properties. At  rst, a novel automaton called zero-forcing (Z-F)  nite automata is de ned according to the notion of a zero-forcing set of a graph. It is shown that for a given graph and for some zero forcing sets, various Z-F- nite automata will be obtained. In addition, the language and the closure properties of Z-F- nite automata, in particular; union, connection, and serial connection are studied. Moreover, considering some properties of graphs such as the closed trail, connected and complete; some new features for Z-F- nite automata are presented. Further, it is shown that there is not any  nite graph such that f be a part of the language of its Z-F- nite automata. Actually, it is proved that for every given graph, the Z-F- nite automata of it does not show any closed trail containing all edges for every zero forcing set, but if the graph G has been a closed trail containing all edges, then the Z-F- nite automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions.

We provide criteria for identifying exact pairs of zero-divisors from zero-divisor graphs of commutative rings, and extend these criteria to compressed zero-divisor graphs. Finally, our results are translated as constructions for exact zero-divisor subgraphs.