Abstract. Introduced by C.~R. Shallon in 1979, graph algebras establish a useful connection between graph theory and universal algebra. This makes it possible to investigate graph varieties and graph quasivarieties, i.e., classes of graphs described by identities or quasi-identities. In this paper, graph quasivarieties are characterized as classes of graphs closed under directed unions of isomorphic copies of finite strong pointed subproducts.

DOI: 10.14232/actasm-019-528-9

AMS Subject Classification (1991): 05C25, 08C15

Keyword(s): graph algebras, quasivarieties

received 29.5.2019, revised 4.3.2020, accepted 6.3.2020. (Registered under 528/2019.)