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Algorithm for Visualization of zero divisor graphs of the Ring ℤ_n Using MAPLE Coding

Open Journal of Discrete Mathematics 2024年第1期14卷 1-8页

作者： Nasir Ali Department of Mathematics Lahore Campus COMSATS University Islamabad Lahore Pakistan Department of Mathematics Vehari Campus COMSATS University Islamabad Vehari Pakistan

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

关键词： zero divisor graph Ring Theory Maple Algorithm ℤn Modulo n graph Theory Mathematical Computing

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Analysis of Distance-Based Topological Polynomials Associated with zero-divisor graphs

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Computers, Materials & Continua 2022年第2期70卷 2895-2904页

作者： Ali Ahmad Roslan Hasni Nahid Akhter Kashif Elahi College of Computer Sciences and Information Technology JazanJazan UniversitySaudi Arabia Faculty of Ocean Engineering Technology and Informatics University Malaysia TerengganuKuala Terengganu21030TerengganuMalaysia Department of Mathematics Govt.College UniversityLahorePakistan Deanship of E-learning and Information Technology Jazan UniversityJazanSaudi Arabia

Chemical compounds are modeled as *** atoms of molecules represent the graph vertices while chemical bonds between the atoms express the *** topological indices representing the molecular graph corresponds to the different chemical properties of *** a,b be are two positive integers,andΓ(Z_(a)×Z_(b))be the zero-divisor graph of the commutative ring Z_(a)×Z_(b).In this article some direct questions have been answered that can be utilized latterly in different *** study starts with simple computations,leading to a quite complex ring theoretic problems to prove certain *** theory of finite commutative rings is useful due to its different applications in the fields of advanced mechanics,communication theory,cryptography,combinatorics,algorithms analysis,and *** this paper we determine the distance-based topological polynomials and indices of the zero-divisor graph of the commutative ring Z_(p^(2))×Z_(q)(for p,q as prime numbers)with the help of graphical structure *** study outcomes help in understanding the fundamental relation between ring-theoretic and graph-theoretic properties of a zero-divisor graphΓ(G).

关键词： zero divisor graph Wiener index Hosoya polynomial (modified)Schulz index (modified)Schulz polynomial

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