Results 191 to 200 of about 1,233,365 (217)

On the zero-divisor graph of Rickart *-rings

Asian-European Journal of Mathematics, 2017
In this paper, we study the zero-divisor graph of Rickart *-rings. We determine the condition on Rickart *-ring so that its zero-divisor graph contains a cut vertex. It is proved that the set of cut vertices form a complete subgraph. We characterize Rickart *-rings for which the complement of the zero-divisor graph is connected. The diameter and girth
Patil, Avinash, Waphare, B. N.
openaire   +2 more sources

Generalized Zero-divisor Graphs

2021
The zero-divisor graph of a commutative ring has been generalized by several authors. The two most notable generalizations are the ideal-based zero-divisor graph and annihilating-ideal graph of commutative rings. We first discuss the ideal-based zero-divisor graph of a commutative ring.
David F. Anderson, T. Asir, Ayman Badawi, T. Tamizh Chelvam   +3 more
openaire   +1 more source

Zero-divisors and zero-divisor graphs of power series rings

Ricerche di Matematica, 2015
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Haouaoui, Amor, Benhissi, Ali
openaire   +2 more sources

Exact Decompositions and Zero-Divisor Graphs

Graphs and Combinatorics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Zero-divisor Graphs of Posets and an Application to Semigroups

Graphs and Combinatorics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dancheng Lu, Tongsuo Wu
openaire   +3 more sources

ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RING

Discrete Mathematics, Algorithms and Applications, 2013
In this paper, we associate the graph ΓI(N) to an ideal I of a near-ring N. We exhibit some properties and structure of ΓI(N). For a commutative ring R, Beck conjectured that both chromatic number and clique number of the zero-divisor graph Γ(R) of R are equal. We prove that Beck's conjecture is true for ΓI(N).
T. Tamizh Chelvam, S. Nithya
openaire   +1 more source

Zero Divisor Graph of a Poset with Respect to an Ideal

Order, 2011
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openaire   +3 more sources

Domination of zero-divisor graphs

Journal of Discrete Mathematical Sciences and Cryptography
The graph that has vertices as elements in a commutative ring R, such that u and v are adjacent only if uv = 0, is called the zero-divisor graph, Π(R). We study the domination of Π(Zn) for all parts of n in this study, since Zn is one of the well-known rings.
Haneen Al-Janabi, Zainab Yasir Alrikabi, Haider Baqer Ameen, Shaymaa Maki Kadham   +3 more
openaire   +1 more source

Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures

Mathematica Slovaca, 2023
Vinayak Joshi, Nilesh Khandekar
exaly  

Zero-divisor graphs and total coloring conjecture

Soft Computing, 2020
Vinayak Joshi, Nilesh Khandekar
exaly