Year: 2021
Author: K. Selvakumar, M. Subajini, S. Pirzada
Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 427–434
Abstract
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 $Γ^n_R$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v54n4.21.07
Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 427–434
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Ring Cayley graph generalized Cayley graph domination number.