Computing the strong metric dimension for co-maximal ideal graphs of commutative rings

Abstract

Let [Formula: see text] be a commutative ring with identity. The co-maximal ideal graph of [Formula: see text], denoted by [Formula: see text], is a simple graph whose vertices are proper ideals of [Formula: see text] which are not contained in the Jacobson radical [Formula: see text] of [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we use Gallai’s Theorem and the concept of strong resolving graph to compute the strong metric dimension for co-maximal ideal graphs of commutative rings. Explicit formulae for the strong metric dimension, depending on whether the ring is reduced or not, are established.