Let (Γ (R)) c be the maximal graph of a commutative ring with identity R whose vertices are
elements of R. Two distinct vertices a and b are adjacent if and only if Ra+ Rb≠ R or there …

INTRODUCTION: This paper addresses the navigation of a team of k protector robots within
pathways, focusing on minimizing the total number of turns. These robots utilize orthogonal …

The researches on topological indices are initially related to graphs obtained from biological
activities or chemical structures and reactivity. Recently, the research on this topic has …

Let R be a commutative ring with identity. The maximal graph of R is the graph whose
vertices are elements of R, where two distinct vertices x and y are adjacent if and only if …

On the Maximal Graph of a Commutative Ring 1. Introduction Page 1 Mathematics
Interdisciplinary Research 8 (3) (2023) 279 − 290 Original Scientific Paper On the Maximal …

Let R be a commutative ring with identity. In this paper we classify rings R such that the
complement of comaximal graph of R is planar. We also consider the subgraph of the …

In this paper, we prove that the study of the comaximal graph of a finite commutative ring
with identity is the same as the study of the zero-divisor graph of the specially constructed …

Let $ R $ be a commutative ring with identity. Let $ G (R) $ denote the maximal graph
associated to $ R $, ie, $ G (R) $ is a graph with vertices as the elements of $ R $, where two …

Let R be a commutative ring with identity. Let Γ (R) denote the maximal graph corresponding
to the non-unit elements of R, ie, Γ (R) is a graph with vertices the non-unit elements of R …

In this paper, with any atomic domain R which admits at least two maximal ideals, we
associate an undirected graph denoted by 𝕄𝔾𝕀 (R) whose vertex set is I (R)={Rπ| π∈ Irr …