Classes of graphs definable by graph algebra identities or quasi-identities
Reinhard Pöschel, Walter Wessel · Czech digital mathematics library · 1987
Graph algebras establish a useful connection between graphs and universal algebras.A graph theoretic characterization of graph quasi-varieties and graph varieties,, resp., i.e. classes of graphs definable by graph algebra quasiidentities and identities, resp., is given.The results are structure theorems of "Birkhoff type": A class of finite undirected graphs is a graph quasi-variety (graph variety, resp.)iff it is closed w.r.t.isomorphisms, Induced subgraphs, finite disjoint unions and homogeneous subproducts (direct products, resp.).Some examples and applications are also considered.