Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks

The molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bond between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. A large number of previous drug experiments revealed that there are strong inherent connections between the drug's molecular structures and the bio-medical and pharmacology characteristics. The forgotten topological index is introduced to be applied into chemical compound and drug molecular structures, which is quite helpful for medical and pharmaceutical workers to test the biological features of new drugs. Such approaches are widely applied in developing areas which are not rich enough to afford the relevant equipment and chemical reagents. In this paper, deals with an interconnection network motivated by molecular structures. The different forms of silicate available in nature lead to the introduction of the dominating silicate network. The first section deals. In this paper, the distinct degrees of enhanced Mesh network, triangular Mesh network, star of silicate network, and rhenium trioxide lattice are listed with drug structure analysis and edge dividing technique, we determine the forgotten polynomial of some molecular structure. The second section contains an algorithm of forgotten polynomial. The third section deals with an application of forgotten polynomial of some drugs.

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“…Suppose that G is a graph of enhanced mesh [13][14][15]. These to fall distinct degrees d u for u ∈ V(EM(m, n)) is {3, 4, 5, 8}.…”

Section: Constructionmentioning

confidence: 99%

Enhanced Mesh Network Using Novel Forgotten Polynomial Algorithm for Pharmaceutical Design

Jeyanthi¹,

Selvarajan²

2022

Intelligent Automation &Amp; Soft Computing

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“…In [29], Mpolynomials and topological indices of V-phenylenic nanotubes and nanotori were evaluated. For some current works on M-polynomials, readers are referred to [30][31][32]. M-Polynomials of circulant graphs were studied in [33].…”

Section: Introductionmentioning

confidence: 99%

Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach

Mondal

Imran

De³

et al. 2023

Complexity

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The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity relationship (QSAR) and quantitative structures property relationship (QSPR) which correlate a molecular structure to its different properties and activities. Graphs containing finite commutative rings have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this article, the topological indices of the total graph T ℤ n n ∈ ℤ + , the zero divisor graph Γ ℤ r n ( r is prime, n ∈ ℤ + ), and the zero divisor graph Γ ℤ r × ℤ s × ℤ t ( r , s , t are primes) are computed using some algebraic polynomials.

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“…Certain topological features of uniform subdivision of Sierpinski networks were calculated in (Liu et al, 2021). General classical valency based topological properties and polynomials of Sierpinski graphs have been determined in (Fan et al, 2021). Two novel degree concepts; edge vertex degree and vertex edge degree notions systematically were defined in (Chellali et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Sierpinski Graflarının Tepe-Ayrıt Temelli Derece Özellikleri Üzerine

Ediz

2023

Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Network science and graph theory are two important branches of mathematics and computer science. Many problems in engineering and physics are modeled with networks and graphs. Topological analysis of networks enable researchers to analyse networks in relation some physical and engineering properties without conducting expensive experimental studies. Topological indices are numerical descriptors which defined by using degree, distance and eigen-value notions in any graph. Most of the topological indices are defined as by using classical degree concept in graph theory, network and computer science. Recently two novel degree parameters have been defined in graph theory: Vertex-edge degree and Edge-vertex degree. Vertex-edge degree and edge-vertex degree based topological indices have been defined as parallel to their corresponding classical degree counterparts. Generalized Sierpinski networks have an important place of applications in view of engineering science especially in computer science. Classical degree based topological properties of generalized Sierpinski graphs have been investigated by many studies. In this article, vertex-edge degree based topological indices values of generalized Sierpinski graphs have been computed.

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Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks

Cited by 3 publications

References 37 publications

Enhanced Mesh Network Using Novel Forgotten Polynomial Algorithm for Pharmaceutical Design

Enhanced Mesh Network Using Novel Forgotten Polynomial Algorithm for Pharmaceutical Design

Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach

Sierpinski Graflarının Tepe-Ayrıt Temelli Derece Özellikleri Üzerine

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