‎Graphs are useful for analysing the structure models in computer science‎, ‎operations‎ ‎research‎, ‎and sociology‎. ‎Also‎, ‎different types of graph products have several applications in‎ ‎modeling‎, ‎including those found in network analysis‎, ‎communication protocols‎, ‎organizational structures‎, ‎diverse fields‎, ‎network analysis and even chemistry‎. ‎In this article‎, ‎we introduce the concept of dominant strong metric dimension of graphs (DSMD for short) as a generalization of strong metric dimension and also dominant metric dimension‎. ‎We determine the DSMD for several families of graphs that include for instance $K_{m,n}$‎, ‎the fan graph $F_{1,n}$‎, ‎the wheel graph $W_{1,n}$ and the helm graph $H_{n}$‎. ‎Additionally‎, ‎we study this invariant under the join product‎, ‎corona product of two graphs and the generalized join graphs‎. ‎Moreover‎, ‎this article investigates the concept of dominant strong metric dimensions for some algebraic graphs associated with rings‎, ‎which is the comaximal graph‎. ‎In fact‎, ‎by using the results on DSMD of the generalized join graphs‎, ‎the dominant strong metric dimension of the comaximal graph of the ring of integers modulo $n$ is investigated‎. ‎Through this exploration‎, ‎besides considering various graph products‎, ‎we aim to provide a comprehensive framework for analyzing commutative rings and their associated graphs‎, ‎thereby‎ ‎advancing both theoretical knowledge and practical applications in diverse domains‎.

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