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Current Organic Synthesis

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ISSN (Print): 1570-1794
ISSN (Online): 1875-6271

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Research Article

Forgotten Topological and Wiener Indices of Prime Ideal Sum Graph of ℤn

Author(s): Esra Öztürk Sözen, Elif Eryaşar and Cihat Abdioğlu*

Volume 21, Issue 3, 2024

Published on: 01 August, 2023

Page: [239 - 245] Pages: 7

DOI: 10.2174/1570179420666230606140448

Price: $65

Abstract

Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge.

Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of ℤn via topological indices is a trending field in spectral graph theory.

Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I + J is a prime ideal of R.

Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of ℤn are calculated for n=pα ,pq, p2q, p2q2, pqr, p3q, p2qr, pqrs where p, q, r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices.

Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.

Keywords: Algorithm, chemical graph theory, forgotten topological index, prime ideal sum graph, topological descriptor, wiener index.

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