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Let $R$ be a commutative ring with identity and $n$ be a natural number. The generalized Cayley graph of $R$, denoted by $Γ^n_R$, is the graph whose vertex set is $R^n$\{0} and two distinct vertices $X$ and $Y$ are adjacent if and only if there exists an $n×n$ lower triangular matrix $A$ over $R$ whose entries on the main diagonal are non-zero such that $AX^T=Y^T$ or $AY^T=X^T$, where for a matrix $B$, $B^T$ is the matrix transpose of $B$. In this paper, we give some basic properties of $Γ^n_R$ and we determine the domination parameters of $Γ^n_R$.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n4.21.07}, url = {http://global-sci.org/intro/article_detail/jms/19296.html} }Let $R$ be a commutative ring with identity and $n$ be a natural number. The generalized Cayley graph of $R$, denoted by $Γ^n_R$, is the graph whose vertex set is $R^n$\{0} and two distinct vertices $X$ and $Y$ are adjacent if and only if there exists an $n×n$ lower triangular matrix $A$ over $R$ whose entries on the main diagonal are non-zero such that $AX^T=Y^T$ or $AY^T=X^T$, where for a matrix $B$, $B^T$ is the matrix transpose of $B$. In this paper, we give some basic properties of $Γ^n_R$ and we determine the domination parameters of $Γ^n_R$.

*Journal of Mathematical Study*.

*54*(4). 427-434. doi:10.4208/jms.v54n4.21.07