By a graph we mean a model of a binary predicate \(\rho(x,y)\). Many well-known properties of binary relations, such as reflexivity, symmetry, antisymmetry, transitivity, etc., are written down by means of quasiidentities. Such important classes of graphs as the class of all partial orders, the class of models of an equivalence relation, the class of all trees, the class of all \(n\)-chromatic graphs, etc. are quasivarieties. Nevertheless, there are very few articles devoted to the study of graphs from the point of view of the theory of quasivarieties of algebraic systems. In the present article we continue the study, initiated by \textit{I. E. Benenson} [Izv. Vyssh. Uchebn. Zaved., Mat. 1979, No. 12(211), 14-20 (1979; Zbl 0432.08007)], of the lattices of quasivarieties and the bases of quasiidentities for some classes of graphs.