Metric dimension of unit graphs

Abstract

The notion of the metric dimension of a graph is well-known and its study is well entrenched in the literature. In this paper, we introduce new classes of graphs that exhibit remarkable characteristic: the metric dimension and the diameter of the unit graph are equal. Additionally, we provide a characterization of finite commutative rings [Formula: see text], wherein the metric dimension assumes a value [Formula: see text], where [Formula: see text]. Further, we also demonstrate an exhaustive examination that ascertains the precise finite commutative rings [Formula: see text], in which domination number is equal to metric dimension of unit graph.