TY - JOUR
T1 - Domination in Generalized Cayley Graph of Commutative Rings
AU - Selvakumar , K.
AU - Subajini , M.
AU - Pirzada , S.
JO - Journal of Mathematical Study
VL - 4
SP - 427
EP - 434
PY - 2021
DA - 2021/06
SN - 54
DO - http://doi.org/10.4208/jms.v54n4.21.07
UR - https://global-sci.org/intro/article_detail/jms/19296.html
KW - Ring, Cayley graph, generalized Cayley graph, domination number.
AB - <p style="text-align: justify;">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&nbsp;$Γ^n_R$ and we determine the domination parameters of&nbsp;$Γ^n_R$.</p>