Hosoya Polynomial and Wiener Index of Zero-Divisor Graph of Z_n

Mohammad, Husam Q.; Authman, Mohammad M. N.

doi:10.33899/csmj.2018.163570

Cited by 8 publications

(6 citation statements)

References 5 publications

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“…In [1] Ahmadi and Jahani-Nezhad first study the Winer index of zero divisor graph of Zn where n=p 2 and p 2 q. In [6] Mohammad and Authman extended this result for n=p m and p m q and study the Hosoya polynomial of this type. In this section we study Hosoya polynomial and Winer index of annihilating-ideal graph of Zn, where n=p m ,p m q and p m q r .…”

Section: On Annihilating -Ideal Graph Of Zp M Q Rmentioning

confidence: 99%

On Annihilating - Ideal Graph of Zn

Mohammad¹,

Younus²

2018

AL-Rafidain Journal of Computer Sciences and Mathematics

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Section: On Annihilating -Ideal Graph Of Zp M Q Rmentioning

confidence: 99%

On Annihilating - Ideal Graph of Zn

Mohammad¹,

Younus²

2018

AL-Rafidain Journal of Computer Sciences and Mathematics

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“…Ahmadi et al (Ahmadi and Nezhad, 2011) in 2011 has provided an algorithm to determining the Wiener index of Z n for n = p 2 , pq. In 2018, Mohammad et al (Mohammad and Authman, 2018) has extended the result by determining the Wiener index of a zero-divisor graph of Γ(Z n ) for n = p m and p m q, where m ∈ Z and m ≥ 2 using the Hosoya polynomial. Pirzada et al (Pirzada et al, 2020) in 2020 determined the Wiener index of a zero-divisor graph and a compressed zero-divisor of Z p m for m ∈ N. In (Asir and Rabikka, 2021), recently a constructed method to calculate the Wiener index of zero-divisor graph of Z n for any positive integer n is determined.…”

Section: Introductionmentioning

confidence: 99%

Complex Networks in Interdisciplinary Research: From Theory to Applications

Zhang,

Wu,

Peron

et al. 2023

Frontiers Research Topics

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Frontiers is more than just an open access publisher of scholarly articles: it is a pioneering approach to the world of academia, radically improving the way scholarly research is managed. The grand vision of Frontiers is a world where all people have an equal opportunity to seek, share and generate knowledge. Frontiers provides immediate and permanent online open access to all its publications, but this alone is not enough to realize our grand goals. Frontiers journal seriesThe Frontiers journal series is a multi-tier and interdisciplinary set of openaccess, online journals, promising a paradigm shift from the current review, selection and dissemination processes in academic publishing. All Frontiers journals are driven by researchers for researchers; therefore, they constitute a service to the scholarly community. At the same time, the Frontiers journal series operates on a revolutionary invention, the tiered publishing system, initially addressing specific communities of scholars, and gradually climbing up to broader public understanding, thus serving the interests of the lay society, too. Dedication to qualityEach Frontiers article is a landmark of the highest quality, thanks to genuinely collaborative interactions between authors and review editors, who include some of the world's best academicians. Research must be certified by peers before entering a stream of knowledge that may eventually reach the public -and shape society; therefore, Frontiers only applies the most rigorous and unbiased reviews. Frontiers revolutionizes research publishing by freely delivering the most outstanding research, evaluated with no bias from both the academic and social point of view. By applying the most advanced information technologies, Frontiers is catapulting scholarly publishing into a new generation. What are Frontiers Research Topics?Frontiers Research Topics are very popular trademarks of the Frontiers journals series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area.

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“…Ahmadi et al ( Ahmadi and Nezhad, 2011 ) in 2011 has provided an algorithm to determining the Wiener index of

for n = p 2 , pq . In 2018, Mohammad et al ( Mohammad and Authman, 2018 ) has extended the result by determining the Wiener index of a zero-divisor graph of

for n = p m and p m q , where

and m ≥ 2 using the Hosoya polynomial. Pirzada et al ( Pirzada et al, 2020 ) in 2020 determined the Wiener index of a zero-divisor graph and a compressed zero-divisor of

for

.…”

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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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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Hosoya Polynomial and Wiener Index of Zero-Divisor Graph of Z_n

Abstract: Let R be a commutative ring with identity. We associate a graph Γ(R). In this paper, we find Hosoya polynomial and Wiener index of Γ(Zn), with n= p m or n= p m q, where p and q are distinct prime numbers and m is an integer with m≥2.

Cited by 8 publications

References 5 publications

On Annihilating - Ideal Graph of Zn

On Annihilating - Ideal Graph of Zn

Complex Networks in Interdisciplinary Research: From Theory to Applications

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

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