Hyperideal-based intersection graphs

Hamidi, Mohammad; Ameri, R.; Mohammadi, Hoda

doi:10.1007/s13226-022-00238-5

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…Hamidi et al introduced the graphs based on the hyperideal of special hyperrings as an extension of graphs based on the ideals of rings. Indeed, they presented graphs based on an ideal of rings to intersection graphs based on the hyperideal of hyperrings for modelling real problems by absorbent elements of hyperrings [11].…”

Section: Introductionmentioning

confidence: 99%

Zero Divisor Graphs Based on General Hyperrings‎

Hamidi

2023

JAHLA

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This paper introduces the concepts of reproduced general hyperring and valued-orderable general hyperring and investigates some properties of these classes of general hyperrings‎. ‎It presents the notions of‎ ‎zero divisors and zero divisor graphs are founded on the absorbing elements of general hyperrings‎. ‎General hyperrings can have more than one zeroing element‎, ‎and therefore‎, ‎based on the zeroing elements‎, ‎multiple zero divisors can be obtained‎. ‎In this study‎, ‎we discuss the isomorphism of zero divisor graphs based on the diversity of divisors of zero divisors‎. ‎The non-empty intersection of the set of absorbing elements and the hyperproduct of zero divisors of general hyperrings play a major role in the production of zero divisor graphs‎. ‎Indeed it investigated a type classification of zero divisor graphs based on the finite general hyperrings‎. ‎We discuss the finite reproduced general hyperrings‎, ‎investigate their zero divisor graphs‎, ‎and show that an infinite reproduced general hyperring can have a finite zero divisor graph‎.

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Section: Introductionmentioning

confidence: 99%

Zero Divisor Graphs Based on General Hyperrings‎

Hamidi

2023

JAHLA

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Hyperideal-based zero-divisor graph of the general hyperring $ \mathbb{Z}_{n} $

Hamidi,

Cristea

2024

MATH

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<abstract><p>The aim of this paper is to introduce and study the concept of a hyperideal-based zero-divisor graph associated with a general hyperring. This is a generalized version of the zero-divisor graph associated with a commutative ring. For any general hyperring $ R $ having a hyperideal $ I $, the $ I $-based zero-divisor graph $ \Gamma^{(I)}(R) $ associated with $ R $ is the simple graph whose vertices are the elements of $ R\setminus I $ having their hyperproduct in $ I $, and two distinct vertices are joined by an edge when their hyperproduct has a non-empty intersection with $ I $. In the first part of the paper, we concentrate on some general properties of this graph related to absorbing elements, while the second part is dedicated to the study of the $ I $-based zero-divisor graph associated to the general hyperring $ \mathbb{Z}_n $ of the integers modulo $ n $, when $ n = 2p^mq $, with $ p $ and $ q $ two different odd primes, and fixing the hyperideal $ I $.</p></abstract>

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Hyperideal-based intersection graphs

Cited by 2 publications

References 21 publications

Zero Divisor Graphs Based on General Hyperrings‎

Zero Divisor Graphs Based on General Hyperrings‎

Hyperideal-based zero-divisor graph of the general hyperring $ \mathbb{Z}_{n} $

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