# Graph quasivarieties

## TL;DR

This paper characterizes graph quasivarieties, classes of graphs defined by quasi-identities, as those closed under directed unions of certain subproducts, bridging graph theory and universal algebra.

## Contribution

It provides a new algebraic characterization of graph quasivarieties using closure properties, extending the understanding of graph classes defined by identities.

## Key findings

- Graph quasivarieties are characterized by closure under directed unions of finite strong pointed subproducts.
- The paper links graph theory with universal algebra through algebraic characterizations.
- Provides a framework for analyzing classes of graphs via algebraic closure properties.

## 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.