Browsing by Author "Chaudhry, Faryal"

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Calculating the Topological Indices of Starphene Graph Via M-Polynomial Approach
(Sami Publishing Co-spc, 2021) Chaudhry, Faryal; Sattar, Sumera; Ehsan, Muhammad; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat
Chemical graph theory is related to the structure of different chemical compounds. A chemical graph represents the molecule of the substance. Chemical graph theory provides the connection between the real number and the different physical, chemical, and biological properties of the chemical species. By implementing the mathematical tools, a chemical graph is converted into a real number. This number can have the predicating ability about the properties of the molecule. In this article, we find some topological indices via M-polynomial for the Starphene graph.
Computational Analysis of New Degree-Based Descriptors of Zig-Zag Benzenoid System
(Sami Publishing Co-spc, 2021) Afzal, Farkhanda; Zaman, Muhammad; Chaudhry, Faryal; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat
Chemical graph theory is one of the dominant branches in graph theory. In this paper, we compute the atom bond connectivity, geometric arithmetic, first K-Banhatti, second K-Banhatti, first K-hyper Banhatti, second K-hyper Banhatti, modified first K-Banhatti, modified second K-Banhatti and harmonic K-Banhatti index via M-polynomial of zig-zag Benzenoid system. We also elaborate the result with graphical representation.
Computing M-Polynomial and Topological Indices of Tuhrc4 Molecular Graph
(Sami Publishing Co-spc, 2021) Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat; Ciftci, Idris
Chemical graph theory has an important role in the development of chemical sciences. A graph is produced from certain molecular structure by means of applying several graphical operations. The local graph parameter is valency, which is defined for every vertex as the number associates with other vertices in a graph, for example an atom in a molecule. The demonstration of chemical networks and chemical compounds with the help of M-polynomials is a novel idea. The M-polynomial of different molecular structures help to compute several topological indices. A topological index is a numeric quantity that describes the whole structure of a molecular graph of the chemical compound and clarifies its physical features, chemical reactivates and boiling activities. In this paper we computed M-Polynomial and topological indices of TUHRC4 Graph, then we recovered numerous topological indices using the M-polynomials.
Degree Based Topological Indices of Tadpole Graph Via M-Polynomial
(Sami Publishing Co-spc, 2021) Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat; Ciftci, Idris
Chemical graph theory has an important impact on the development of the chemical sciences. A chemical graph is a graph that is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with the M-polynomials is a revolution and the M-polynomial of different molecular structures contributes to evaluating many topological indices. In this paper we worked out M-Polynomial and topological indices of the tadpole graph, then we recovered numerous topological indices using the M-polynomials.
Degree-Based Entropy of Molecular Structure of Hac5c7[P,q]
(Sami Publishing Co-spc, 2021) Afzal, Farkhanda; Cancan, Murat; Ediz, Suleyman; Afzal, Deeba; Chaudhry, Faryal; Farahani, Mohammad Reza
This study aimed at using the calculated values of topological indices, degree weighted entropy of graph, the entropy measures are calculated viz., symmetric division index, inverse sum index atom-bond connectivity entropy and geometric arithmetic entropy for the nanotube HAC(5)C(7)[p,q].
Exploring Metric Dimensions in Chemical Structures : Insights and Applications
(Taru Publications, 2025) Chaudhry, Faryal; Maktoof, Mohammed Abdul Jaleel; Mousa, Sura Hamed; Farooq, Umar; Farahani, Mohammad Reza; Alaeiyan, Mehdi; Cancan, Murat
In this article, we dive into the metric dimension of various lattice networks, focusing on Bakelite, Backbone DNA, and Polythiophene networks. The metric dimension is a crucial graph invariant that helps us understand how uniquely we can identify the vertices in a network. Our detailed analysis and calculations reveal that the metric dimension for Bakelite, Polythiophene, and Backbone DNA networks is consistently two. This means that, within these lattice structures, a simple pair of vertices is enough to pinpoint the location of all other vertices. These insights shed light on the structural properties of these molecular networks and could have practical implications for areas like biological systems and organic electronics. Plus, this study sets the stage for future research in graph theory and the understanding of molecular structures.
Investigating the Metric and Edge Metric Dimensions of H-Naphthalenic Nanotubes
(Taru Publications, 2025) Chaudhry, Faryal; Afzal, Deeba; Hussein, Noor Mejbel; Abbas, Azhar Ali; Abbas, Wasim; Farahani, Mohammad Reza; Cancan, Murat
If the distances between two vertices in a simple connected network are different, then a vertex x resolves the pair u and v. A set S of vertices in G is referred to as a resolving set if every pair of distinct vertices in G can be identified by at least one vertex in S. The metric dimension (MD) of G is the minimum number of vertices required for a resolving set. Moreover, an edge metric generator is any subset S of vertices that can distinguish between any two distinct edges, e1 and e2, according to their respective distances. An edge metric dimension (EMD), dime(G), is an edge metric generator of the least size. This study aims to explore the metric dimension (MD) and edge metric dimension (EMD) of the H-Naphthalenic Nanotube.
M-Polynomials and Degree-Based Topological Indices of Tadpole Graph
(Taylor & Francis Ltd, 2021) Chaudhry, Faryal; Husin, Mohamad Nazri; Afzal, Farkhanda; Afzal, Deeba; Cancan, Murat; Farahani, Mohammad Reza
Chemical graph theory is a branch of mathematical chemistry which has an important outcome on the development of the chemical sciences. A chemical graph is a graph which is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with M-polynomials is a new idea and the M-polynomial of different molecular structures supports us to calculate many topological indices. A topological index is a numeric quantity that describes the whole structure of a molecular graph of the chemical compound and supports to understand its physical features, chemical reactivates and boiling activities. In this paper, we compute M-polynomial and topological indices of tadpole graph, then we recover numerous topological indices using the M-polynomial.
M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide
(Hindawi Ltd, 2021) Chaudhry, Faryal; Shoukat, Iqra; Afzal, Deeba; Park, Choonkil; Cancan, Murat; Farahani, Mohammad Reza
Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randic index and inverse Randic index, and the augmented Zagreb index using calculus.
On Computation of M-Polynomial and Topological Indices of Starphene Graph
(Taru Publications, 2021) Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
Chemical graph theory is a sub field of mathematical chemistry that is very beneficial in the progress of the computational analysis of the chemical compounds. A chemical graph is the outcome of the molecular structure by applying some graph The demonstration of chemical compounds with the M-polynomials is a developing idea and the M-polynomial of different molecular structures supports us to calculate many topological indices. In this paper we calculate M-polynomial and topological indices for the starphene graph, then we recover numerous topological indices using the M-polynomials.
On Metric Dimension of Circumcoronene Series of Benzenoid Networks
(Taru Publications, 2025) Chaudhry, Faryal; Abbas, Azhar Ali; Maktoof, Mohammed Abdul Jaleel; Farooq, Umar; Farahani, Mohammad Reza; Alaeiyan, Mehdi; Cancan, Murat
In molecular topology and chemistry, resolving sets and metric bases are essential concepts. They have numerous applications in computer science, artificial intelligence, chemistry, pharmacy, traffic networking, mathematical modeling, and programming. Adivision S of the vertex set chi of a linked graph G is said to resolve G if eachpoint of G can be represented from its neighborhood in S. A metric dimension of a graph is the number of the smallest resolving set, also known as the metric basis of the graph.In the current research we will determine the metric dimension and metric basis of the circumcoronene series CS of benzenoid Hk for k >= 1. We prove that a set with three vertices is required to resolve this graph, and therefore, its metric dimension is 3.
On Topological Aspects of Silicate Network Using M-Polynomial
(Taylor & Francis Ltd, 2021) Afzal, Farkhanda; Alsinai, Ammar; Hussain, Sabir; Afzal, Deeba; Chaudhry, Faryal; Cancan, Murat
M-polynomial is introduced as a graph polynomial to re-cover closed formulas of degree based topological indices by using some suitable operators. These topological indices have a predicting ability about the properties of organic molecules. Silicate network (phyllosilicates) belonging to an important group of minerals that includes talc, micas, serpentine, clay, and chlorite minerals. These minerals have much importance in the chemical industry. The aim of this paper is to explore the silicate network through M-polynomial and some degree-based topological indices. Results are also elaborated by plotting with graphs.
Some New Degree Based Topological Indices of H-Naphtalenic Graph Via M-Polynomial Approach
(Sami Publishing Co-spc, 2021) Afzal, Farkhanda; Alsinai, Ammar; Zeeshan, Mohammad; Afzal, Deeba; Chaudhry, Faryal; Cancan, Murat
In this object, we present some new formulas of the reduced reciprocal Randic index, the arithmetic geometric 1 index, the SK, SK1, SK2 indices, first Zagreb index, the general sum-connectivity index, the SCI index and the forgotten index. They were utilized for new degree-based topological indices via M-polynomial. We retrieved these topological indices for H-Naphtalenic nanotubes.
Topological Analysis of Zigzag-Edge Coronoid Graph by Using M-Polynomial
(Sami Publishing Co-spc, 2021) Ehsan, Muhammad; Sattar, Sumera; Chaudhry, Faryal; Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat
The chemical graph theory is interrelated with the chemical structure of different compounds. This graph represents the molecule of the sub-stance. A chemical graph is rehabilitated into a real number by applying some mathematical tackles. This number can elaborate on the properties of the molecule. This number is called topological catalogs. Here, we find some topological catalogs via M-polynomial for the zigzag-edge coronoid graph.
Topological Indices of the System of Generalized Prisms Via M-Polynomial Approach
(Sami Publishing Co-spc, 2021) Afzal, Farkhanda; Farahani, Mohammad Reza; Cancan, Murat; Arshad, Faiza; Afzal, Deeba; Chaudhry, Faryal
The characteristics of various networks can be distinguished with the help of topological indices. The purpose of this paper is to study the generalized prism network, which is very interesting for physics and engineering researchers. Regarding this network, we recovered some degree-based topological indices from the Mpolynomial. We measured topological indices such as atom-bond connectivity, geometric arithmetic, K Banhatti, K hyper Banhatti, modified K Banhatti and harmonic K Banhatti by using Mpolynomial approach.