Results 61 to 70 of about 180 (93)

THE TOTAL GRAPH OF A MODULE OVER A COMMUTATIVE RING WITH RESPECT TO PROPER SUBMODULES

, 2012
Let R be a commutative ring and M be an R-module with a proper submodule N. The total graph of M with respect to N, denoted by T(ΓN(M)), is investigated.
AHMAD ABBASI, SHOKOOFE HABIBI
core   +1 more source

Minimal submodules graph of modules over commutative rings [PDF]

Let R be a commutative ring and M be an R-module. In this paper, we define minimal submodules graph of M , denoted by Γmin(M ), in which the vertex set is the set of nonzero proper submodules of M .
Ismiarti, Dewi, Anam, Syaiful, Mahanani, Dwi Mifta   +2 more
core   +1 more source

ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A PARTIALLY ORDERED SET

, 2017
In this paper, it is proved that the complement of the zero-divisor graph of a partially ordered set is weakly perfect if it has finite clique number, completely answering the question raised by Joshi and Khiste [‘Complement of the zero divisor graph of ...
VINAYAK JOSHI, SARIKA DEVHARE, JOHN LAGRANGE   +2 more
core   +1 more source

The Submodule-Based Zero-Divisor Graph with Respect to Some Homomorphism

, 2013
Let M be an R-module and 0 6= f ∈ M∗ = Hom(M, R). The graph Γf (M) is a graph with vertices Z f (M) = {x ∈ M \ {0} | xf(y) = 0 or yf(x) = 0 for some non-zero y ∈ M}, in which non-zero elements x and y are adjacent provided that xf(y) = 0 or yf(x ...
M. Baziar, N. Ranjbar
core  

On the connectedness of the complement of the zero-divisor graph of a poset

, 2019
In this paper, connectedness is completely characterized for the complements of the zero-divisor graphs of partially ordered sets. These results are applied to annihilating ideal graphs and intersection graphs of submodules, generalizing some of the work
Joshi, Vinayak, LaGrange, John, Devhare, Sarika   +2 more
core  

The large sum graph related to comultiplication modules

, 2018
Let $R$ be a commutative ring and $M$ be an $R$-module. We define the large sum graph, denoted by $\acute{G}(M)$, as a graph with the vertex set of non-large submodules of $M$ and two distinct vertices are adjacent if and only if $N+K$ is a non-large ...
Ansari-Toroghy, Habibollah, Mahboobi-Abkenar, Farideh   +1 more
core  

Core Knowledge Learning Framework for Graph

Graph classification is a pivotal challenge in machine learning, especially within the realm of graph-based data, given its importance in numerous real-world applications such as social network analysis, recommendation systems, and bioinformatics ...
Xu, Guangning, Xiao, Mingyan, Huang, Hu, Huang, Zhichao, Zhang, Bowen, Fan, Xiaomao, Dai, Genan   +6 more
core   +1 more source

Exploring Geometrical Properties of Annihilator Intersection Graph of Commutative Rings

Let Λ denote a commutative ring with unity and D(Λ) denote a collection of all annihilating ideals from Λ. An annihilator intersection graph of Λ is represented by the notation AIG(Λ).
Ali Al Khabyah, Moin A. Ansari
core   +1 more source

g-Small Intersection Graph of a Module

    لتكن  حلقة ابدالية أحادية، وليكن   مقاساً ايسر احادي. بيان تقاطع صغير من النمط-g للمقاس  يرمز له  ,  هو بيان غير مباشر بسيط رؤوسه تقابل كل المقاسات الجزئية غير التافهة في  وكل رأسين مختلفين متجاورين أذا وفقط أذا كان التقاطع بينهما هو صغير من النمط-g.
Alwan, Ahmed H.
core   +1 more source

Metric dimension and Zagreb indices of essential ideal graph of a finite commutative ring

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}.
A V, Chithra, P, Jamsheena
core