Browsing by Author "Farahani, Mohammad Reza"

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Bounds on Partition Dimension of Peterson Graphs
(Taylor & Francis Ltd, 2021) Khalaf, Abdul Jalil M.; Nadeem, Muhammad Faisal; Azeem, Muhammasd; Cancan, Murat; Farahani, Mohammad Reza
The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (theta(1), theta(2), ..., theta(t)}. A vertex eta is an element of V(P), and r(eta vertical bar theta) = {d(eta, theta(1)), d(eta, theta(2)), ...., d(eta, theta(t))} be a l - tuple distances, where r(eta vertical bar theta) is the representation of a vertex eta with respect to set theta. If r(eta vertical bar theta) of eta is unique, for every pair of vertices, then theta is the resolving partition set of V(P). The minimum number l in the resolving partition set theta is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, P-lambda,P-lambda-1 and proved that these families have bounded partition dimension.
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.
Computational Techniques in Machine Learning, Fuzzy Systems, Image Processing and Signal Analysis
(Taru Publications, 2025) Farahani, Mohammad Reza; Alaeiyan, Mehdi; Ameen, Hayder Baqer; Zhang, Xiujun; Cancan, Murat; Afzal, Farkhanda
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.
Construction of Petersen Graph Via Graph Product and Correlation of Topological Descriptors of Petersen Graph in Terms of Cyclic Graph C5
(Taylor & Francis Ltd, 2022) Waheed, Muhammad; Saleem, Umair; Cancan, Murat; Tas, Ziyattin; Alaeiyan, Mehdi; Farahani, Mohammad Reza
Graph product yields a new structure from two initial given structures. The computation of topological indices for these sophisticated structures using the graph product is a critical endeavor. Petersen graph is a structure which consists of ten vertices and fif teen edges. It is commonly used as a counter example to graph theory conjectures. In this paper, we generate simple Petersen graph by using graph product and then explicit expressions of the first and second Zagreb indices, forgotten topological index, first hyper and first reformulated Zagreb index, reduced second Zagreb index and Y-index of the Peterson graph in terms of cyclic graph C-5 are computed.
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 Distance Based Topological Indices of Some Graph Transforms
(Taylor & Francis Ltd, 2022) Patil, Shobha, V; Hosamani, Sunilkumar M.; Shirkol, Shailaja S.; Cancan, Murat; Farahani, Mohammad Reza; Kalynashetti, Manjula
A topological index is invariantly used to study the structure of molecular graph. In this paper, we have generalized degree distance index, Gutman index and reciprocal degree distance index, and calculate generalized indices for splitting and co-splitting graphs.
Degree-Bad Topological Descriptors of Star of David and Hexagonal Cage Networks
(Sami Publishing Co-spc, 2020) Ali, Haidar; Shafiq, Muhammad Kashif; Farahani, Mohammad Reza; Cancan, Murat; Aldemir, Mehmet Serif
Topological indices are numerical parameters of a graph that characterize its molecular topology. In theoretical chemistry, the numerical parameters which are used to depict the molecular topology of graphs are called topological indices. Several physical and chemical properties like boiling point, entropy, heat-formation and vaporization enthalpy of chemical compounds can be determined through these topological indices. Graph theory has a considerable use in evaluating the relation for various topological indices of some derived graphs. In this paper, we studied the general Randic first Zagreb, ABC, GA, ABC(4) and GA(5), indices for the Star of David and Hexagonal Cage networks and provided closed formulas of these indices.
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.
The First and Second Zagreb Polynomial and the Forgotten Polynomial of Cmxcn
(Sami Publishing Co-spc, 2020) Afzal, Farkhanda; Afzal, Deeba; Baig, Abdul Qudair; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
In this paper, the 1st and 2nd Zagreb polynomials and the forgotten polynomial of C(m)xC(n) were computed. Some degree-based topological indices such as 1st and 2nd multiple Zagreb indices, Hyper Zagreb index and the forgotten index or F-index of the given networks were also computed. In addition, we represented the outcome by graphical representation that describe the dependence of topological indices on the given parameters of polynomial 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.
Leap Indices and Their Polynomials of the Derived Graph of the Subdivision of Certain Polyphenyls
(Sami Publishing Co-spc, 2020) Asif, Fatima; Zahid, Zohaib; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
Topological indices are real (numerical) values which are associated with chemical compositions to correlate with chemical structure with different physical properties, chemical and biological activities. In this article, we computed and compared leap Zagreb indices and leap hyper-Zagreb indices of the derived graph of the subdivision of certain polyphenyls based on the 2-distance degree of the vertices.
M-Polynomial and Degree-Based Topological Indices and Line Graph of Hex Board Graph
(Sami Publishing Co-spc, 2020) Amin, Shahid; Rehman, Muhammad Aziz Ur; Aldemir, Mehmet Serif; Cancan, Murat; Farahani, Mohammad Reza
A topological index (TI) is a positive real number associated with the graph of molecule and remains invariant up to graph isomorphism. Until now, several TIs are defined and there are mainly three types: Degree depending, distance depending and spectrum depending. All these TIs found huge applications in pharmacy, theoretical chemistry and especially in QSPR/QSAR research. The aim of our study was to compute degree depending TIs for Hex board graph and its line graph. We firstly computed M-polynomial and by applying calculus, we computed several degree-based topological indices of Hex board graph and its line graph.
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.
More Topological Indices of Generalized Prism Network
(Analytic Publ Co, 2020) Cancan, Murat; Ediz, Suleyman; Fareed, Saba; Farahani, Mohammad Reza
Networks plays an important role in the field of engineering and topological indices can help us to get interesting properties if of underlined networks. With the help of topological indices, one can understand the topology and differentiate properties of different networks. The aim of this paper is to study the Generalized prism network which is very important for the researchers working in physics and engineering. We computed several degree-based indices, for example, sum connectivity index, Arithmetic-Geometric index, modified Randic, SK index, SK1 index, and SK2.
Multiplicative Degree-Based Topological Indices and Line Graph of Hex Board Graph
(Sami Publishing Co-spc, 2020) Amin, Shahid; Rehman, Muhammad Aziz Ur; Farahani, Mohammad Reza; Cancan, Murat; Aldemir, Mehmet Serif
Mathematical chemistry is the area of research in mathematics, in which problems of chemistry are solved by utilizing techniques of mathematics. In mathematical chemistry, a number is assigned to molecular graph of compound called topological index (TI) which depends on the topology of compound and helps us in deciding properties of concerned compound. TIs usually depend on the degree of vertices in a graph, distances and spectrum, among which degree depending TIs are studied extensively in recent years and have led to huge applications in theoretical chemistry, drugs formulation and pharmacy. This paper aimed to compute some degree depending TIs of Hex board networks and line graph of hex board networks. The generalized first and second multiplicative Zagreb indices (ZIs), multiplicative version of Atomic bond connectivity index (ABC) and generalized multiplicative Geometric Arithmetic index (GA) of Hex board and the line graph of Hex board networks were computed in this study.
New Degree-Based Topological Descriptors Via M Polynomial of Boron Α-Nanotube
(Sami Publishing Co-spc, 2020) Afzal, Deeba; Hussain, Sabir; Aldemir, Mehmet Serif; Farahani, Mohammad Reza; Afzal, Farkhanda
The study of molecular structure having size less than 100 nm is called nanotechnology. Nano-materials have vast applications in different fields. Boron alpha-nanotube is very famous in Nano-science. In this article, we computed some important topological indices of this structure using their M-polynomial along with plotting the results.