Metric and upper dimension of zero divisor graphs associated to commutative rings

Acta Universitatis Sapientiae: Informatica

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