Topics concerning metric dimension related invariants in graphs are nowadays intensively
studied. This compendium of combinatorial and computational results on this topic is an …

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 connected graph G (V, E), a vertex w ∈ V (G) w∈ V (G) strongly resolves two vertices
u, v ∈ V (G) u, v∈ V (G) if there exists a shortest uw uw path containing v or a shortest vw vw …

Let R be a commutative ring with non-zero identity and W^*(R) W∗(R) be the set of all non-
zero and non-unit elements of R. The cozero-divisor graph of R, denoted by Γ^ ′ (R) …

Zero-divisor graphs of finite commutative rings: a survey Page 1 Surveys in Mathematics and
its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 15 (2020), 371 – 397 …

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 …

The zero-divisor graph Γ (R) of a commutative unital ring R is the (simple undirected) graph
whose vertex set is all zero divisors of R except 0 R and two distinct vertices are joined by an …

Let R be a commutative ring with identity. The zero-divisor graph of R denoted by Γ (R) is an
undirected graph Γ (R)=(V (Γ), E (Γ)), where V (Γ) is the set of non-zero zero-divisors of R …

The metric representation of a vertex v of a graph G is a finite vector representing distances
of v with respect to vertices of some ordered subset W⊆ V (G). The set W is called a minimal …

The concept of metric dimension is derived from the resolving set of a graph, that is measure
the diameter among vertices in a graph. For its usefulness in diverse fields, it is interesting to …