This article investigates the concept of dominant metric dimensions in zero divisor graphs
(ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as …

For a finite commutative ring $ R $ with identity $1\neq 0$, the zero divisor graph $\Gamma
(R) $ is a simple connected graph having vertex set as the set of nonzero zero divisors of …

For a finite commutative ring $\mathbb {Z} _ {n} $ with identity $1\neq 0$, the zero divisor
graph $\Gamma (\mathbb {Z} _ {n}) $ is a simple connected graph having vertex set as the …

Let R be a commutative ring with all non-zero zero divisors Z∗(R) of R. Then Γ (R) is said to
be a zero divisor graph if and only if a· b= 0 where a, b∈ V (Γ (R))= Z∗(R) and (a, b)∈ E (Γ …

The A γ matrix of a graph G is determined by A γ (G)=(1− γ) A (G)+ γ D (G), where 0≤ γ≤ 1,
A (G) and D (G) are the adjacency and the diagonal matrices of node degrees, respectively …

For a finite group G, the power graph P (G) is a simple connected graph whose vertex set is
the set of elements of G and two distinct vertices x and y are adjacent if and only if xi= y or …

For a finite commutative ring Zn with identity 1= 0, the zero divisor graph Γ (Zn) is a simple
connected graph having vertex set as the set of non-zero zero divisors, where two vertices x …

Let R be a finite commutative ring with non zero identity. The unit graph of R denoted by G
(R) is the graph obtained by setting all the elements of R to be the vertices of a graph and …

A topological index is a numeric quantity associated with a chemical structure that attempts
to link the chemical structure to various physicochemical properties, chemical reactivity, or …

For a finite group G, the power graph P (G) is a simple connected graph whose vertex set is
the set of elements of G and two distinct vertices are adjacent if and only if one is a power of …