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International Journal of Algebra, Vol. 6, 2012, no. 24, 1147 - 1162 Hyperidentities in (X(YZ))Z with Opposite Loop and Reverse Arc Graph Varieties of Type (2,0) Montri Thongmoon 1 and Tiang Poomsa-ard 2 Department of Mathematics, Faculty of Science Mahasarakham University, Mahasarakham 44150, Thailand montri.t@msu.ac.th1 , tiang@kku.ac.th2 Abstract Graph algebras establish a connection between directed graphs with- out multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies a term equation s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = Mod Σ where Σ is a subset of T (X ) × T (X ). A g graph variety V = Mod Σ is called (x(yz))z with opposite loop and g reverse arc graph variety if Σ is a set of (x(yz))z with opposite loop and reverse arc term equation. A term equation s ≈ t is called an identity in a variety V if A(G) satisfies s ≈ t for all G ∈ V. An identity s ≈ t of a variety V is called a hyperidentity of a graph algebra A(G), G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations of A(G) of the appropriate arity, the resulting identities hold in A(G). An identity s ≈ t of a variety V is called a hyperidentity of V if it is a hyperidentity of A(G) for all G ∈ V. In this paper we characterize all hyperidentities of each (x(yz))z with opposite loop and reverse arc graph variety.