Results 91 to 100 of about 1,283,848 (178)

The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring

Contemporary Mathematics and Applications (ConMathA)
The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero.
Jinan Ambar, I Gede Adhitya Wisnu Wardhana, Abdurahim   +2 more
doaj   +1 more source

Graph Decomposition Techniques in Neutrosophic Zero Divisor Models of Commutative Ring [PDF]

Neutrosophic Sets and Systems
This research establishes the framework for neutrosophic zero divisor graphs, extending the capabilities of existing fuzzy zero divisor graph models. While fuzzy models account for partial uncertainty through degrees of membership, they often fail to ...
K. Gunasekar, P. Muralikrishna
doaj   +1 more source

Wiener index of an ideal-based zero-divisor graph of commutative ring with unity

AKCE International Journal of Graphs and Combinatorics
The Wiener index of a connected graph G is [Formula: see text]. In this paper, we obtain the Wiener index of H-generalized join of graphs [Formula: see text]. As a consequence, we obtain some earlier known results in [Alaeiyan et al. in Aust. J.
Balamoorthy S., Kavaskar T., Vinothkumar K   +2 more
doaj   +1 more source

C 4 -free zero-divisor graphs

, 2013
. In this paper we give a characterization for all commutative rings with 1 whose zero-divisor graphs are C4 ...
Sayyed Heidar Jafari
core  

Induced subgraphs of zero-divisor graphs

, 2022
The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with $a$ and $b$ adjacent if $ab=0$. We show that the class of zero-divisor graphs is universal, in the sense that every
Chelvam, T. Tamizh, Arunkumar, G., Cameron, Peter J., Kavaskar, T.   +3 more
core  

Characterizations Of Zero Divisor Graphs Determined By Equivalence Classes Of Zero Divisors [PDF]

, 2012
We study zero divisor graphs of commutative rings determined by equivalence classes of zero divisors, specifically for a Noetherian ring R. We study the classification of these graphs.
Acosta, Amanda Catherine
core  

Zero-divisor Graphs of Localizations and Modular Rings

, 2008
In this paper, we examine the algebraic properties of localizations of commutative rings and how localizations affect the zero-divisor graph’s structure of modular rings.
Young, William, Lokken, Kathryn A., Cuchta, Tom   +2 more
core  

ZERO-DIVISOR GRAPHS OF ÖRE EXTENSION RINGS

, 2011
Let R be an associative ring with two-sided multiplicative identity. In this paper, in the case that R is a commutative α-compatible ring, we compare the diameter (and girth) of the zero-divisor graphs Γ(R) and Γ(R[x;α, δ]).
M. R. KHORSANDI, K. KHASHYARMANESH, M. AFKHAMI   +2 more
core   +1 more source

Diameter of Zero Divisor Graphs of Finite Direct Product of Lattices

, 2014
In this paper, we verify the diameter of zero divisor graphs with respect to direct ...
V. V. Joshi, H. Y. Pourali, B. N. Waphare.   +2 more
core   +1 more source

Zero-divisor graphs of direct products of commutative rings

, 2006
We recall several results of zero divisor graphs of commutative rings. We then examine the preservation of diameter and girth of the zero divisor graph of direct products of commutative ...
Warfel, Joseph, Stickles, Joe, Axtell, Michael   +2 more
core