Metric and Strong Metric Dimension in Cozero-Divisor Graphs

Abstract

Let R be a commutative ring with non-zero identity and $$W^*(R)$$ be the set of all non-zero and non-unit elements of R. The cozero-divisor graph of R, denoted by $$\Gamma ^{\prime }(R)$$ , is a graph with the vertex set $$W^*(R)$$ and two distinct vertices a and b are adjacent if and only if $$a\not \in Rb$$ and $$b\not \in Ra$$ . In this paper, the metric dimension and strong metric dimension of $$\Gamma ^{\prime }(R)$$ are investigated. We compute the exact values of strong metric and metric dimension in cozero-divisor graphs of reduced rings. Moreover, the metric dimension in cozero-divisor graphs of non-reduced rings is discussed.