Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs

The strongly annihilating-ideal graph SAG(R) of a commutative unital ring R is a simple graph whose vertices are non-zero ideals of R with non-zero annihilator and there exists an edge between two distinct vertices if and only if each of them has a non-zero intersection with annihilator of the other one. In this paper, we compute twin-free clique number of SAG(R) and as an application strong metric dimension of SAG(R) is given. Moreover, we investigate the structures of strong resolving sets in SAG(R) to find forcing strong metric dimension in SAG(R) .