We determine the metric dimension of the annihilating-ideal graph of a local finite
commutative principal ring and a finite commutative principal ring with two maximal ideals …

In this paper, we investigate the Sombor index of the zero-divisor graph of Zn which is
denoted by Γ (Zn) for n∈{pα, pq, p2q, pqr} where p, q and r are distinct prime numbers …

Topological indices are numerical values in graphs. Recently, they have been an attractive
topic and multidisciplinary research area in mathematics, computer science, chemistry …

The main objective of this paper is to calculate the forgotten topological index of the zero-
divisor graph of $\mathbb {Z} _n $. Let $ p $, $ q $ and $ r $ be distinct prime numbers. We …

The idempotent divisor graph of a commutative ring R is a graph with vertices set in R*= R-
{0}, and any distinct vertices x and y are adjacent if and only if xy= e. For some non-unit …

Let $ R $ be a commutative ring with unity. The essential ideal graph $\mathcal {E} _ {R} $ of
$ R $ is a graph whose vertex set consists of all nonzero proper ideals of\textit {R}. Two …

Let 𝕍 be a vector space over a field ℱ with basis ℬ={α 1, α 2,…, α n}. Let W be an m-
dimensional subspace of 𝕍 with basis {α w 1, α w 2,…, α wm}, where α wi is some α j∈ ℬ …

The metric dimension problem is called navigation problem due to its application to robot
navigation in space. Further this concept has wide applications in motion planning, sonar …

The idempotent divisor graph of a commutative ring R is a graph with vertices set in R*= R-
{0}, and any distinct two vertices v and u in it are adjacent, say vu, if and only if vu= e, for …

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 …