Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings

This paper investigates the inclusion ideal graph of a commutative unitary ring R, denoted as In(R), which is defined by its vertices representing all non-trivial ideals of R. The edges of the graph connect two distinct vertices if one ideal is a proper subset of the other. We explore the strong metric dimension of In(R), providing a comprehensive characterization of its strong resolving graph. Additionally, we compute the metric dimension of In(R), illustrating the implications of our findings on the structure of the graph and its applications in the study of ideal theory within commutative rings.