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 …

A topological index is a numerical descriptor in mathematical chemistry and graph theory
that quantifies a molecule's structural properties without considering its three-dimensional …

Let n≥ 1 be a fixed integer. The main objective of this paper is to compute some topological
indices and coindices that are related to the graph complement of the prime ideal sum (PIS) …

For a commutative ring $ R, $ with non-zero zero divisors $ Z^{\ast}(R) $. The zero divisor
graph $\Gamma (R) $ is a simple graph with vertex set $ Z^{\ast}(R) $, and two distinct …

Let G be a simple graph with vertex set V (G)(| V (G)|= n) and let S⊆ V (G). We denote by di,
the degree of the vertex vi. The graph GS is obtained from G by removing all the vertices …

In the present article, we give the distance spectrum of the zero divisor graphs of the
commutative rings Zt [x]/⟨ x4⟩(t is any prime), Zt2 [x]/⟨ x2⟩(t≥ 3 is any prime) and Ft [u] …

Let G be a simple graph on n vertices with vertex set V (G). The energy of G, denoted by,
$\mathcal {E}(G) $ is the sum of all absolute values of the eigenvalues of the adjacency …

‎ Let $\mathcal {R} $ be the commutative ring $\mathcal {R}=\mathbb {Z} _ {p^ 2}[x]/\langle
x^{2}\rangle $ with identity and ${Z^{*}}(\mathcal {R}) $ be the set of all non-zero zero …

Let R be a commutative ring with 1. A zero-divisor graph Λ (R) is an undirected graph on the
vertex set R−{0} such that any two nonzero elements p, q∈ R are adjacent whenever p⋅ q …