The study of hyperstructures derived from particular mathematical objects is very important and interesting. Graph theory has been established as a fundamental and important tool for solving practical problems in other branches of mathematics. This paper can be considered as one of the connections between hyperstructures and graph theory. In this way, by using the dominating set notion of a graph, we define a hyperoperation on verticals of it and study its properties and then we construct a hypergroup based on this hyperoperation. This hypergroup is presented for some classes of graphs.