# HYPERIDENTITIES IN (xy)x ≈x(yy) GRAPH ALGEBRAS OF TYPE (2,0)

• Khampakdee, Jeeranunt (DEPARTMENT OF MATHEMATICS MAHASARAKHAM UNIVERSITY) ;
• Poomsa-Ard, Tiang (DEPARTMENT OF MATHEMATICS MAHASARAKHAM UNIVERSITY)
• Published : 2007.11.30
• 78 5

#### 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 an identity $s{\approx}t$ if the corresponding graph algebra $\underline{A(G)}$ satisfies $s{\approx}t$. A graph G=(V,E) is called an $(xy)x{\approx}x(yy)$ graph if the graph algebra $\underline{A(G)}$ satisfies the equation $(xy)x{\approx}x(yy)$. An identity $s{\approx}t$ of terms s and t of any type ${\tau}$ is called a hyperidentity of an algebra $\underline{A}$ if whenever the operation symbols occurring in s and t are replaced by any term operations of $\underline{A}$ of the appropriate arity, the resulting identities hold in $\underline{A}$. In this paper we characterize $(xy)x{\approx}x(yy)$ graph algebras, identities and hyperidentities in $(xy)x{\approx}x(yy)$ graph algebras.

#### Keywords

identities;hyperidentities;term;normal form term;binary algebra;graph algebra;$(xy)x{\approx}x(yy)$ graph algebra

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#### Cited by

1. IDENTITIES IN BIREGULAR LEFTMOST GRAPH VARIETIES OF TYPE (2,0) vol.02, pp.01, 2009, https://doi.org/10.1142/S1793557109000029
2. Graph variety generated by linear terms pp.1793-7183, 2018, https://doi.org/10.1142/S1793557119500748