期刊论文详细信息
Acta Universitatis Sapientiae: Informatica | |
Metric and upper dimension of zero divisor graphs associated to commutative rings | |
Aijaz M.1  Pirzada S.2  | |
[1] Department of Mathematics, University of Kashmir, India;University of Kashmir, Srinagar, India; | |
关键词: ring; zero divisor; zero divisor graph; metric dimension; upper dimension; 13a99; 05c78; 05c12; | |
DOI : 10.2478/ausi-2020-0006 | |
来源: DOAJ |
【 摘 要 】
Let R be a commutative ring with Z*(R) as the set of non-zero zero divisors. The zero divisor graph of R, denoted by Γ(R), is the graph whose vertex set is Z*(R), where two distinct vertices x and y are adjacent if and only if xy = 0. In this paper, we investigate the metric dimension dim(Γ(R)) and upper dimension dim+(Γ(R)) of zero divisor graphs of commutative rings. For zero divisor graphs Γ(R) associated to finite commutative rings R with unity 1 ≠ 0, we conjecture that dim+(Γ(R)) = dim(Γ(R)), with one exception that R≅Π
【 授权许可】
Unknown