Browsing by Author "Dr. Kashif Ali"

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Algebraic Characteristics of Graphs
(Library Information Services COMSATS University Islamabad Lahore Campus, 2020) Muhammad Asim Razzaq; FA13-PMATH-004; LHR TP 7454; Dr. Kashif Ali
Graph theory is a vital and special branch of discrete mathematics. It deals with geometric computational study of various objects. The main component and object of the theory is graph and its generalization approach. Therefore, it has vast application to other mathematical and provides computational assistance to non-mathematical sciences. The most prominent use of graph theory as a significant tool in chemistry, this branch is named as chemical graph theory. It provides helpful assistance for obtaining molecular descriptor to develop essential relationship between molecular graphs and chemical compounds. Graph theory also serves its specialization in algebraic graph theory specifically labellings. In this dissertation, we formulate and discuss all these types of indices. We develop a new approach to calculate the eccentricities of vertices of any graph by using computer aid softwares. This approach help us to find the exact expression of the ECI and ABC5 for the butterfly, bene and torodial grid graphs. We also express a new type of counting polynomial associated with the previous counting polynomials. Moreover, we work some topological indices relative to degree dependent on generalized subdivision of line graphs. We also determine the general results about subdivision of line graphs for neighborhood valency-based indices. We also discuss the stability of line graph of chemical molecules.”Line0graphs furnish0a tool for0studying the0topological properties of0alpha-systems.”In addition to this, we study four important counting polynomials called omega, theta, PI and Sadhana for V-Phenylenic. We also introduced a new polynomial Upsilon on the basis of ”co” relation and find new results relative to new counting polynomial.”We also determine that inertia indices for V-phenylenic nanotube and these indices are not0equal for the line0graph of V-phenylenic0nanotube. We also find that the0nullity for this0nanotube and of line0graph of these0nanotube.”Lastly, we also discuss H-group magic labellings of some graphs. We mainly study about the H-groupmagic0total graph0labelings G(v; e) over finite0abelian0group Zt Zv, where H =K2; Ct and e = (t 􀀀1)v:
Analytical and Soliton Solutions for Nonlinear Schr dinger Equation
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Badar Nawaz; CIIT/FA13-PMATH-001/LHR; Dr. Kashif Ali; LHR TP 5941
A soliton which is also known as the traveling wave solution has a unique property,” the collision of two solitons produce the waves whose permanent structure remain the same”. These wave solutions are very stable and having a key role in the mathematical physics, especially in ﬁber technology. ”A soliton does not change its amplitude, shape and speed for a long distance in a non-local and nonlinear optical media”. The applications of soliton solutions are also in various branches of physics. The soliton solutions can be calculated by using the different types of nonlinearities. The optical solitons are very important in the study of nonlinear optical ﬁbers. In this thesis ﬁrstly, we determine different types of soliton solutions of dimensionless form of Quintic Complex Ginzburg-Landau (CGLQ) equation by using modiﬁed extended tanh− function method (METFM) and the extended trial equation method (ETEM). Sec- ondly, we obtain bright, singular and Jacobi elliptic soliton solutions for the time fractional perturbed NLSE (TFPNLSE) by using ETEM with Kerr, power and log law nonlineari- ties. Thirdly, we ﬁnd the combo and dipole soliton solutions for CGLQ model with differ- ent ansatz methods. Next, we construct different soliton solutions for the paraxial NLSE (PNLSE) in Kerr media by ETEM. Then, we get the bright and dark solitons for non- Kerr law NLSE with third order (3OD) and fourth order (4OD) dispersions by Sine-cosine method (SCM)and Bernoullis equation method (BEM) with nonlinearities. In the last, by using Hirota bilinear method (HBM), we obtain the multiple solitons for the nonlinear Telegraph equation (NLTE) and the nonlinear PHI-four equation (NLPFE).
Computational Invariants of Some Chemical Structures
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Abdur Rehman Hashmi; CIIT/FA19-RMT-004/LHR; Dr. Kashif Ali; LHR TP 7435
In this study we will focus on computational invariants of different structures of chemical graphs. We will focus on the bond additive invariant, new bond additive invariant especially Mostar invariant, edge Mostar invariant and Total Mostar invariants of some graphs like Hydrogen Depleted molecular graph of Vulcanized Rubber and Poly-Methyl Methacrylate(PMMA).
Connection Numbers of Some Graphs
(Library Information Services COMSATS University Lahore Campus, 2024-03-13) Muhammad Usama Arshad; FA22-RMT-041; Dr. Kashif Ali; LHR TP 9363
In this study, we apply different graph operations to find the dual graphs of different chem ical structures including honey comb graph, Boron tube graph , Boron nano tube graph and Silicate network. Then we will find the connection numbers of these mentioned graphs and after that we will find 1st, 2nd and modified ZCI (Zagreb connection indices).
DEGREE BASE TOPOLOGICAL INDICES OF SOME FAMILIES OF GRAPHS
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Mahrukh; SP15-RMT-009; LHR TP 6828; Dr. Kashif Ali
Atopological index is a numerical value associated with chemical constitution for cor relation of chemical structure with various physical properties, chemical reactivity or biological activity. In this thesis, we will discuss the different degree based topological indices i.e. Randic index, Zagreb index, Atom-bond connectivity index, Geometric arithmetic index, Augmented Zagreb index, Harmonic index, Sum-connectivity index for benzene BCZ, Benzene BTA diamond like graph, line graph of ladder and line graph of nanostar dendrimers. We will also compute ABC4 and GA5 for benzene BCZ, Benzene BTA diamond like graph
Entropy Measure of Degree Based Indices for the Boron Nanotubes
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Shahid; CIIT/SP20-RMT-006/LHR; Dr. Kashif Ali; LHR TP 7624
The physicochemical properties of molecules are correlated with their chemical struc- ture using degree-based topological indices. The graph entropy zone has captured the imagination of scientists because of its possible application in chemistry. Boron nan- otubular structures are high-interest materials with new electronic characteristics due to the presence of multi center bonds. Mechanical and thermal stability are two chal- lenges that these materials have in nanodevice applications. Therefor they necessitate theoretical research into the other qualities. In this thesis, study the graph entropy mea- sure by using topological invariants of different versions of atom-bond connectivity in- dex Zagreb indices M1(G), M2(G) (including redeﬁned forms ReZG1(G), ReZG2(G) and ReZG3(G) and the forgotten topological index F(G)) which gives a better predic- tion of the chemical properties of different chemical compounds. We computed these indices for boron nanotube because of its signiﬁcance in nanotechnology. To ensure the correctness of the output, a computational analysis and graphical comparison of generated indices is provided.
Entropy Measure Of Degree Based Invariants …
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Maryam Saber; FA19-RMT-034; LHR TP 7381; Dr. Kashif Ali
Chemical graph theory is a branch of mathematical chemistry that uses graph theory techniques mathematically create the chemical phenomena. In addition, chemical graph theory refers to the applications of graph theory to solve molecular chain. In the field of chemical research this theory has important applications. In this thesis, we find the some topological indices and the estimated values of these indices. We determine some entropy of degree based indices of different chemical structures especially the dendrimers and para-line graph and we research the entropies of the graph linked to a new information function accessible. We explore topological indices M1(G)andM2(G), the redefined form of Zagreb indices, the F-index F(G);R(G) index of the molecular chain especially the dendrimers. Furthermore, we compare the predicted values of these indices and give the graphical representation of these indices.
Group H-magic labelings of graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2015) Syed Tahir Raza Rizvi; FA11-PMT-002; Dr. Kashif Ali; LHR TP 5283
A simple graph G admits an H-covering if each edge in E G is a member of a sub- graph of G isomorphic to H. An H-magic labeling of a graph G possessing an H-covering is a bijective function from the vertex-set and the edge-set of the graph G onto the set 1 2 V G E G if there occurs a positive integer , called the magic sum, such that for every subgraph H of G isomorphic to H, the sum wt H v V H v e E H e is equal to . The sum wt H is termed as, the H-weight. A graph is called H-magic (H-supermagic) if it possesses an H-magic (H-supermagic) labeling. If H is isomorphic to K2, then resulting labeling is known as edge-magic total labeling. This dissertation studies about the formulation of cycle-supermagic labelings for the disjoint union of isomorphic and non isomorphic copies of different families of graphs. We also evaluate the K2-supermagic labelings of some families of alpha trees. More- over, we ﬁnd the cycle-(super)magic labelings of uniform subdivided graph and cycle- supermagic labelings for non uniform subdivisions of fans and triangular ladders graphs. We also articulate about the introduction of H-groupmagic total labeling of a graph G over a ﬁnite abelian group A . In this study, we determine the H-groupmagic total labelings of fan graphs and disjoint union of isomorphic as well as non-isomorphic copies of fan graphs over ﬁnite abelian group A 3 n, where n 3
H-Irregular Total Labeling Of Connected Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Kaleem; FA19-RMT-028; Dr. Kashif Ali; LHR TP 7390
A labelling α is a vertex H irregular k-labelling of graph in which we assign the value from {1, 2, 3, · · · , k} to the vertices for this the weight of Hi and Hj is different for i 6= j. The vertex weight of any H can be calculated by adding the labels of the vertices which are includes in H. A labelling α is edge H irregular k-labelling α of graph in which we assign the value from {1, 2, 3, · · · , k} to the edges for this the weight of Hi and Hj is different for i 6= j. The weight of any H can be calculated by adding the labels of edges which are includes in H. In this thesis we ﬁnd the vertex and edge H irregular k-labellings of Starphene graph, ladder graph, triangular ladder graph and double gear graph. Key words: The vertex and edge H irregular k-labellings starphene graph and gear graph.
On Degree Based Topological Indices of Calcium Oxide
(Library Information Services, CUI Lahore, 2022) Muhammad Faisal Hanif; FA20-RMT-035; Dr. Kashif Ali
Graph Theory is playing a key role in applied and pure mathematics. The scope of Graph Theory is expanding day by day. In this thesis, we compute some topological indices, Co-indices and reverse degree-based indices such as first and second Zagreb Coindex, first and second multiplicative Zagreb coindex, forgotten topological coindex, atom bond connectivity coindex, geometric arithmetic Oxide. My thesis comprising of five chapters. In the 1st chapter, we will define some basic definitions and literature review. In the 2nd chapter, we will find topological Indices of Calcium Oxide structure. In the 3rd chapter, we will find topological Co-Indices of Calcium Oxide structure. In the 4th chapter, we will find the reverse degree based topological Indices of Calcium Oxide. In the 5th chapter, we will present the conclusion of our thesis.
On Some Topological Indices of Manganese Oxide Graphs
(Library Information Services, CUI Lahore, 2022) FA20-RMT-031; Sanaullah; Dr. Kashif Ali
Graph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In this thesis, we have evaluated some degree based topological indices, namely, the geometric arithmetic index, the hyper Zagreb index, the forgotten index, the first and second Zagreb indices, the first and second multiple Zagreb indices, the redefined first, second and third Zagreb indices for Maganese dioxide Mno2 and its para-line graph. My thesis comprising of six chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find degree based topological indices for Maganese dioxide Mno2 and its para-line graph In the 3rd chapter, we will find degree based topological Co- indices for Maganese dioxide Mno2 and its para-line graph. In the 4th chapter, we will find degree based topological Reverse indices for Maganese dioxide Mno2 and its para-line graph.
Physicochemical Properties of Some Drugs by Using Machine Learning
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Amman Farzeen; CIIT/SP24-RMT-023/LHR; Dr. Kashif Ali; LHR TP 10083
This study explores the integration of machine learning and multi-criteria decision-making techniques for the characterization and evaluation of potential therapeutics targeting Duchenne Muscular Dystrophy . A dataset comprising the physicochemical properties of twenty anti- Duchenne muscular dystrophy drug candidates is analyzed using topological indices de- rived from molecular graphs. These indices, computed via Python-based algorithms, served as input features for machine learning models. Artificial Neural Networks and Random Forests are employed to predict key physicochemical properties based on the structural de- scriptors. The results demonstrate that topological indices are effective predictors, enabling accurate and consistent performance across both models. To prioritize the drug candidates, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied as an multi-criteria decision-making tool, leveraging the model predictions to rank compounds based on multiple beneficial attributes. The proposed framework highlights the synergy be- tween graph-theoretical descriptors, machine learning, and multi-criteria decision-making, offering a robust in-silico approach for early-stage drug evaluation. This methodology pro- vides a systematic and objective strategy for ranking therapeutic candidates, particularly valuable in the context of rare diseases such as duchenne muscular dystrophy. Key words: Machine learning; Molecular Graph; QSPR Analysis; Topological indices; Ar- tificial Neural Networks; Random Forest; TOPSIS; Python Algorithm; Anti-DMD drugs.
Predicting Physicochemical Properties of Various Drugs with Machine Learning’s Algorithms
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Tamseela Ashraf (FA23-RMT-04); Dr. Kashif Ali; LHR TP 9785
Machine learning methods are useful in computational chemistry by providing powerful tools for predicting the properties and activities of chemical structures. Diverse drugs with such variety in chemical structure and biological activity pose signiﬁcant challenges for traditional drug discovery methods. However, that working with machine learning algo- rithms we can process sets of various drugs and ﬁnd patterns to uncover hidden patterns and relationships. Concerning this analysis, important descriptors are the topological in- dices that characterize various structural features of molecular graphs. These indices offer mathematical expression for the molecule topology, capturing information regarding the connection and position of the atoms within the molecule. This work aims to establish the role of machine learning together with various drugs and the topological indices in order to enhance the ability of drug discovery and development. Key words: Machine learning Algorithms; Molecular Graph; QSPR Analysis; Topological indices; Artiﬁcial Neural Networks; Random Forest; Python Algorithm; Antiviral drugs.
Resolving Topological Index Of Graphs Associated
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Ali Bahadar; FA19-RMT-109; Dr. Kashif Ali; LHR TP 7394
In this thesis, we study a well-known concept of graph theory, called resolvability, in con- text of two types of graphs ( commuting and non-commuting) associated to two algebraic structures (dihedral and semi-dihedral groups). By analyzing the resolving share and the average resolving share of each vertex, we compute the resolving topological index of each graph.
Some Topological Invariants for Extended Para Line Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Abaid Ur Rehman; SP19-RMT-017; LHR TP 6474; Dr. Kashif Ali
Some Topological Polynomials of Transformed Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Bilal Ahmad; SP19-RMT-030; LHR TP 6480; Dr. Kashif Ali
Zagreb Connection Indices for Some Benzenoid Systems
(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Kiramat Ali; FA22-RMT-049; Dr. Kashif Ali; LHR TP 9386
A benzenoid system is a molecular structure discovered in organic chemistry that compris esa planar, cyclic arrangement of carbon atoms connected by alternating single and double bonds. Polycyclic hydrocarbons, heterocyclic compounds, and organic molecules with fused rings can all contain benzenoid system. A benzenoid system is a finite connected subgraph of an infinite hexagonal lattice that has neither non-hexagonal internal faces nor cut vertices. The ultimate goal is to derive mathematical formulas for first, second and modified Zagreb connection indices for the line graph of k-subdivided of six benzenoid systems(three pericondensed and three catacondensed systems). In the end, we compute graphical and numerical comparisons between the first, second, and modify Zagreb con nection indices of these systems