Prime Decomposition of Zero Divisor Graph in a Commutative Ring

Kuppan, A.; Sankar, J. Ravi

doi:10.1155/2022/2152513

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Since topological indices are the numerical quantity of a network and are invariant under graph isomorphisms, researchers are interested in examining the physical properties and symmetries of algebraic structures through graph representations, similar to those in chemistry. In addition, graphs constructed from rings are finite structures, and finite rings and fields have received a significant amount of focus for their applications in cryptography and coding theory [37][38][39]. In [40][41][42], the authors computed vertex-based eccentric and edge-based topological indices of zero-divisor graphs of Z pq × Z r , where p, q, and r are primes.…”

Section: Motivation Behind Topological Indices Over Algebraic Graphsmentioning

confidence: 99%

Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings

Öztürk Sözen,

Alsuraiheed,

Abdioğlu

et al. 2023

Symmetry

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Let n≥1 be a fixed integer. The main objective of this paper is to compute some topological indices and coindices that are related to the graph complement of the prime ideal sum (PIS) graph of Zn, where n=pα,p2q,p2q2,pqr,p3q,p2qr, and pqrs for the different prime integers p,q,r, and s. Moreover, we construct M-polynomials and CoM-polynomials using the PIS-graph structure of Zn to avoid the difficulty of computing the descriptors via formulas directly. Furthermore, we present a geometric comparison for representations of each surface obtained by M-polynomials and CoM-polynomials. Finally, we discuss the applicability of algebraic graphs to chemical graph theory.

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Section: Motivation Behind Topological Indices Over Algebraic Graphsmentioning

confidence: 99%

Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings

Öztürk Sözen,

Alsuraiheed,

Abdioğlu

et al. 2023

Symmetry

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“…Zaid et al [20] computed the two finite rings with zero divisors, which are the ring of two-by-two matrices over integers modulo two and three. Kuppan and Ravi Sankar [21] presented a prime decomposition of a zero divisor graph in a commutative ring in the year 2022. This paper presents the theoretical results for constructing a new general formula of the first Zagreb index of a zero divisor graph using the set of integers modulo power of primes, ℤ 𝑝 𝑘 .…”

Section: Introductionmentioning

confidence: 99%

The First Zagreb Index of the Zero Divisor Graph for the Ring of Integers Modulo Power of Primes

Semil @ Ismail,

Sarmin,

Alimon

et al. 2023

Mal. J. Fund. Appl. Sci.

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Let be a simple graph with the set of vertices and edges. The first Zagreb index of a graph is defined as the sum of the degree of each vertex to the power of two. Meanwhile, the zero divisor graph of a ring , denoted by , is defined as a graph with its vertex set contains the nonzero zero divisors in which two distinct vertices and are adjacent if . In this paper, the general formula of the first Zagreb index of the zero divisor graph for the commutative ring of integers modulo , where a prime number and a positive integer is determined. A few examples are given to illustrate the main results.

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Roadmap for Competitive Production of Solid‐State Batteries: How to Convert a Promise into Reality

Pacios

Villaverde

Valenzuela

et al. 2023

Advanced Energy Materials

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This work describes the most logical approach to address the imminent scale up and mass industrial manufacturing of solid‐state batteries (SSBs) attending to material, product and production requirements. All the currently used technologies, starting from small lab scale and going to initial prototyping and industrial attempts, are evaluated against exclusion criteria focused on achieving a low‐cost, high throughput, reliable and easily scalable manufacturing process that is in addition environmentally friendly and minimizes risk related to human health and work safety. Batteries that rely on raw materials which are readily available and are ethically produced. Batteries that are manufactured using energy that leaves no carbon footprint and are efficiently reused and recycled, resulting in minimal impact on the earth’s resources and climate. Batteries that do not exist today but will certainly exist tomorrow. The resulting roadmap is used as the benchmark to compare the manufacturing strategies of the main industrial players attempting mass fabrication of SSBs in the next 5–10 years

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Prime Decomposition of Zero Divisor Graph in a Commutative Ring

Abstract: Let R be a commutative ring and let Γ Z n be the ze… Show more

Cited by 4 publications

References 8 publications

Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings

Computing Topological Descriptors of Prime Ideal Sum Graphs of Commutative Rings

The First Zagreb Index of the Zero Divisor Graph for the Ring of Integers Modulo Power of Primes

Roadmap for Competitive Production of Solid‐State Batteries: How to Convert a Promise into Reality

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