Properties of (x(yz))z with Opposite Loop and Reverse Arc Graph Varieties of Type (2,0)

Mittree Krapeedang, Tiang Poomsa-ard

Abstract

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph $G$ satisfies a term equation $s \approx t$ if the corresponding graph algebra $\underline{A(G)}$ satisfies $s \approx t$. A class of graph algebras $\mathcal{V}$ is called a graph variety if $\mathcal{V} = Mod_g \Sigma$ where $\Sigma$ is a subset of $T(X) \times T(X)$. A graph variety $\mathcal{V'} = Mod_g\Sigma^{'}$ is called an $(x(yz))z$ with opposite loop and reverse arc graph variety if $\Sigma^{'}$ is a set of $(x(yz))z$ with opposite loop and reverse arc term equations.In this paper, we characterize all $(x(yz))z$ with opposite loop and reverse arc graph varieties.