The Wiener index of the zero-divisor graph of a finite commutative ring with unity

Selvakumar, K.; Gangaeswari, P.; Arunkumar, G.

doi:10.1016/j.dam.2022.01.012

Cited by 24 publications

(15 citation statements)

References 4 publications

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“…In this paper, we are interested in the parameter Wiener index of graphs for the rings of integers modulo p s q t . Although the formulas in the general case for the rings of

have been obtained in literatures ( Asir and Rabikka, 2021 ) and ( Selvakumar et al, 2022 ), compared with their results, our formula is more direct and convenient for calculation the Wiener index

. We also get the formula for compressed zero-divisor graph.…”

Section: Introductionmentioning

confidence: 96%

“…The authors of ( Asir and Rabikka, 2021 ) calculated the complete formula through restrict n as product of distinct primes and the remaining cases. In 2022, Selvakumar et al ( Selvakumar et al, 2022 ) visualized the zero-divisor graph Γ( R ) as a generalized composition of suitable choices of graphs and derived a formula for the Wiener index of the graph

.…”

Section: Introductionmentioning

confidence: 99%

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The wiener index of the zero-divisor graph for a new class of residue class rings

Wei

Luo

2022

Front. Chem.

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The zero-divisor graph of a commutative ring R, denoted by Γ(R), is a graph whose two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0. The main problem of the study of graphs defined on algebraic structure is to recognize finite rings through the properties of various graphs defined on it. The main objective of this article is to study the Wiener index of zero-divisor graph and compressed zero-divisor graph of the ring of integer modulo psqt for all distinct primes p, q and s,t∈N. We study the structure of these graphs by dividing the vertex set. Furthermore, a formula for the Wiener index of zero-divisor graph of Γ(R), and a formula for the Wiener index of associated compressed zero-divisor graph ΓE(R) are derived for R=Zpsqt.

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“…In this paper, we are interested in the parameter Wiener index of graphs for the rings of integers modulo p s q t . Although the formulas in the general case for the rings of

have been obtained in literatures ( Asir and Rabikka, 2021 ) and ( Selvakumar et al, 2022 ), compared with their results, our formula is more direct and convenient for calculation the Wiener index

. We also get the formula for compressed zero-divisor graph.…”

Section: Introductionmentioning

confidence: 96%

.…”

Section: Introductionmentioning

confidence: 99%

The wiener index of the zero-divisor graph for a new class of residue class rings

Wei

Luo

2022

Front. Chem.

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show abstract

“…These properties may include the algebraic properties of the zero divisor graphs and the physio chemical properties of the chemical structures. By adopting this strategy, several researchers studied different objects such as algebraic objects [1], pysio-chemical properties of chemical structures [2][3][4], drugs used for breast cancer treatment [5], and interconnection networks [6]. The analysis of networks, such as Butterfly network [7], Benes network [8,9], Interconnection network [6,10] and David-derived network [11] through similar approach, is one of the most recent developments in the field of graph theory.…”

Section: Introductionmentioning

confidence: 99%

On Some Ev-Degree and Ve-Degree Dependent Indices of Benes Network and營ts Derived Classes

Wang¹,

Arshad²,

Fahad³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks, Benes networks, Interconnection networks, and David-derived networks using graph theoretic parameters. The topological indices (TIs) have been widely used as graph invariants among various graph theoretic tools. Quantitative structure activity relationships (QSAR) and quantitative structure property relationships (QSPR) need the use of TIs. Different structure-based parameters, such as the degree and distance of vertices in graphs, contribute to the determination of the values of TIs. Among other recently introduced novelties, the classes of ev-degree and ve-degree dependent TIs have been extensively explored for various graph families. The current research focuses on the development of formulae for different ev-degree and ve-degree dependent TIs for s− dimensional Benes network and certain networks derived from it. In the end, a comparison between the values of the TIs for these networks has been presented through graphical tools.

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“…Determining the various topological indices of graphs associated with different algebraic structures has became an interesting area of research in the past few years. To get a better un-derstanding about this, refer [4,15,18]. Being motivated from this, we determine the wiener index of the essential ideal graph of a finite commutative ring.…”

Section: Introductionmentioning

confidence: 99%

Adjacency Spectrum and Wiener Index of the Essential Ideal Graph of a Finite Commutative Ring $\mathbb{Z}_{n}$

Jamsheena¹,

Chithra²

2023

Preprint

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Let R be a commutative ring with unity. The essential ideal graph of R, denoted by E R , is a graph with vertex set consisting of the set of all nonzero proper ideals of R and two vertices I and K are adjacent if and only if I + K is an essential ideal. In this paper, We determine the adjacency spectrum and wiener index of the essential ideal graph of the finite commutative ring Z n , for n = p m 1 and n = p m 1 q m 2 , where p and q are distinct primes with p < q and m 1 , m 2 are positive integers.

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The Wiener index of the zero-divisor graph of a finite commutative ring with unity

Cited by 24 publications

References 4 publications

The wiener index of the zero-divisor graph for a new class of residue class rings

The wiener index of the zero-divisor graph for a new class of residue class rings

On Some Ev-Degree and Ve-Degree Dependent Indices of Benes Network and營ts Derived Classes

Adjacency Spectrum and Wiener Index of the Essential Ideal Graph of a Finite Commutative Ring $\mathbb{Z}_{n}$

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