Browsing by Author "Afzal, Deeba"

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Algorithm for Computing Differential Char Sets Efficiently
(Taru Publications, 2020) Cancan, Murat; Afzal, Farkhanda; Maqbool, Ayesha; Afzal, Deeba
In order to triangularize differential polynomial sets and systems, we can use char sets method by Ritt and Wu. This method uses differential pseudo division for elimination of variables successively. In this paper, we have proved that Differential Pseudo division can be replaced by important reductions for computing differential char sets. An algorithm is presented for computing the differential char sets efficiently. This algorithmic scheme has been executed with precise admissible differential reductions. Primary results demonstrate that this new algorithm accomplishes better results than char set algorithm that are based on differential Pseudo division.
Characteristic Sets Verses Generalized Characteristic Sets
(Taru Publications, 2021) Afzal, Farkhanda; Akram, Safia; Ashiq, Muhammad; Afzal, Deeba; Cancan, Murat; Ediz, Suleyman
The notion of characteristic sets that was developed by Ritt and Wu has been turned into an usual tool for study of set/systems of polynomial equations, algebraic as well as differential equations. By constructing a characteristic sets, one can triangularize an arbitrary set/system of any type of polynomials. It ensures that it can be decomposed into triangular form of a particular set/system. In this manuscript, a comparison of characteristic sets defined by Ritt-Wu's differential is provided with the generalized characteristic sets defined by author in [5]. Comparison shows that this scheme performs better than earlier method.
Closed Formulas of Topological Properties for Remdesivir (C27h35n6o8p)
(Sami Publishing Co-spc, 2021) Hussain, Sabir; Alsinai, Ammar; Afzal, Deeba; Maqbool, Ayesha; Afzal, Farkhanda; Cancan, Murat
Coronavirus is able to cause illnesses ranging from the common flu to severe respiratory disease. Today there is great competition among researchers and physcisians to cure COVID-19. Remdesivir is being studied for the COVID-19 treatment In this article, we presented the topological analysis of remdesivir with the help of M-polynomial. Proofs of the closed form of some topological indices via M-polynomial are also included in this article. [GRAPHICS] .
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.
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].
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.
An Improved Fast Error Convergence Topology for Pdα-Type Fractional-Order Ilc
(Taylor & Francis Ltd, 2021) Riaz, Saleem; Lin, Hui; Mahsud, Minhas; Afzal, Deeba; Alsinai, Ammar; Cancan, Murat
The monotonic convergence of the PD alpha-type fractional-order iterative learning control algorithm is considered for a class of fractional-order linear systems. First, a theoretical analysis of the monotonic convergence of 1st and 2nd order PD alpha-type control algorithms is carried out in the typical terms of Lebesgue-p (L-p), and the sufficient conditions for their monotonic convergence are comprehended and extended to the case of N-order control algorithms; then the speed of convergence of the two is explained in detail. It is concluded that the conditions for convergence of the control algorithm are determined by the learning gain and the system's properties are together determined. Simulation experiment verifies the accuracy of proposed scheme and the validity of the control algorithm.
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-Polynomial and Topological Indices Poly (Ethyleneamidoamine) Dendrimers
(Analytic Publ Co, 2020) Cancan, Murat; Ediz, Suleyman; Mutee-Ur-Rehman, Hafiz; Afzal, Deeba
Dendrimers are constructed by the successive addition of layers of branching groups. Topological indices are numerical numbers associated which are graph invariant up to isomorphism. In this report, we give closed form of M-polynomial of PETAA dendrimers and from this M-polynomial, we recover many topological indices. These topological indices help to predict physcio-chemical properties of the underling dendrimers, and help to the study of the properties of the materials of ship building. We also give graphical representation of our results.
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.
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.
On Computation of Latest Topological Descriptors of Some Cactus Chains Graphs Via M-Polynomial
(Taylor & Francis Ltd, 2021) Afzal, Farkhanda; Hussain, Hina; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
In the field of chemical graph theory, topological indices are of great importance. The topological index is a numerical quantity dependent on different invariants or molecular graph characteristics. In the present article, the topological indices of para cacti chain graph are calculated such as 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 using their M-polynomials by the formulas given in [2]. Graphical analysis of the findings is also displayed. capability to recover the topological indices.
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 Computation of Newly Defined Degree-Based Topological Invariants of Bismuth Tri-Iodide Via M-Polynomial
(Taylor & Francis Ltd, 2021) Hameed, Saira; Husin, Mohamad Nazri; Afzal, Farkhanda; Hussain, Hina; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat
In this article, we recover many degree-based topological invariants using their formulas given in table [1] of Bismuth Tri-iodide by using its M-polynomial. The M-polynomial is a new phenomenon by which we can easily compute topological invariants of molecular graph. This is a very well-known fact that topological invariants play a key role in deciding chemical compound properties. Graphical analysis of the findings is also displayed.
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.
Some New Topological Indices of Silicate Network Via M-Polynomial
(Taru Publications, 2020) Cancan, Murat; Afzal, Deeba; Hussain, Sabir; Maqbool, Ayesha; Afzal, Farkhanda
The numerical encoding of chemical structure with topological indices is currently growing in chemical graph theory. An important aspect of these topological indices related with the prediction of the characteristic given by the chemical structure of the molecule. This paper utilizing a specific developed method, named M-polynomial, to calculate the topological indices of silicate network. We also plot the topological indices.
A Study of Newly Defined Degree-Based Topological Indices Via M-Polynomial of Jahangir Graph
(Taru Publications, 2021) Afzal, Deeba; Ali, Samia; Afzal, Farkhanda; Cancan, Murat; Ediz, Suleyman; Farahani, Mohammad Reza
There is an incredible importance of topological indices in the field of graph theory. M-polynomial is a very effective way for finding the topological indices of a graph. In this article, some important topological indices such as Atom bond connectivity index, geometric-arithmetic index, K-Banhatti indices, Hyper K-Banhatti indices and Modified K-Banhatti indices of Jahangir graph has been calculated from its M-polynomial.
A Study of Non-Commutative Von-Neumann Regular Rings
(Taylor & Francis Ltd, 2021) Afzal, Farkhanda; Rukh, Shah; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
In this paper, we study the Von-Neumann regular elements of non-commutative rings M-2(Z(2)) and M-2(Z(3)). We prove that M-2(Z(2)) and M-3(Z(3)) are Von-Neumann rings. We also give code in C++ to compute Von-Neumann regular elements of M-2(Z(n)).