Coloring in essential annihilating-ideal graphs of commutative rings

R Nikandish, M Mehrara, MJ Nikmehr - Soft Computing, 2024 - Springer
The essential annihilating-ideal graph EG (R) of a commutative unital ring R is a simple
graph, whose vertices are non-zero ideals of R with non-zero annihilator and there exists an …

[PDF][PDF] On the genus of strong annihilating-ideal graph of commutative rings

M Nazim, N ur Rehman… - Asian-European Journal …, 2023 - researchgate.net
Let R be a commutative ring with unity and A (R) be the set of annihilating-ideals of R. The
strong annihilating-ideal graph of R, denoted by SAG (R), is an undirected graph with vertex …

Characterization of rings with genus two prime ideal sum graphs

P Mathil, J Kumar - arXiv preprint arXiv:2308.04048, 2023 - arxiv.org
Let $ R $ be a commutative ring with unity. The prime ideal sum graph of the ring $ R $ is a
simple undirected graph whose vertex set is the set of nonzero proper ideals of $ R $ and …

[PDF][PDF] On the genus and crosscap of the total graph of commutative rings with respect to multiplication

M Nazim, C Abdioglu, N Rehman… - Journal of Algebra and …, 2024 - researchgate.net
Let S be a commutative ring and Z (S) be its zerodivisors set. The total graph of S with
respect to multiplication, denoted by TZ (S)(Γ (S)), is an undirected graph with vertex set as …

[PDF][PDF] On the genus of annihilator intersection graph of commutative rings

M Nazim, NU Rehman, K Selvakumar - Algebraic Structures and Their …, 2024 - sid.ir
Let R be a commutative ring with unity and A (R) be the set of annihilatingideals of R. The
annihilator intersection graph of R, represented by AIG (R), is an undirected graph with A …

Analysis of Some Topological Indices Over the Weakly Zero-Divisor Graph of the Ring

N ur Rehman, SA Mir, M Nazim - … on Associative Rings and Algebras with …, 2022 - Springer
In this paper, we study some basic properties of weakly zero-divisor graph of the ring Z p× Z
q× Z r, denoted by W Γ (Z p× Z q× Z r), where p, q and r are prime numbers greater than 2 …

[引用][C] ON THE ESSENTIAL IDEAL GRAPHS AASOCIATED TO COMMUTATIVE RINGS

A Altaf - Korean J. Math, 2023