    - Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors       Hyperidentities in $(xy)x approx x(yy)$ graph algebras of type $(2,0)$ Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 651-661 Published online December 1, 2007 Jeeranunt Khampakdee and Tiang Poomsa-ard Mahasarakham University, Mahasarakham University Abstract : Graph algebras establish a connection between directed gra-phs 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 MSC numbers : 05C25, 08B15 Downloads: Full-text PDF