Final Year Projects (FYPs) - Undergraduates

Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/53

This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.

Browse

Now showing 1 - 20 of 128

A study of generlazied scound law of Themodaynamic in masssive Gravity
(2024) Muhammad Shoib ( Sp 21- BSM-024), Muhammad Awais (sp21- BSM-002); Dr. Rabia Saleem; LHR TP -9878
A Study of Triglyceride by Using Topological Indices
(Library Information Services, CUI Lahore, 2023) Ali Ahmad; FA20-RMT-007; Dr. Hafiz Muhammad Afzal Siddiqui
A topological graph index, also called a molecular descriptor, is a mathematical formula that can be applied to any graph which provides the information about its chemical properties. From this index, it is possible to analyse mathematical values and further investigate some physicochemical properties of a molecule. Therefore, it is an efficient method in avoiding expensive and time-consuming laboratory experiments. In this thesis, we study some degree based topological indices of triglyceride its line and paraline graphs.
An Introduction to Projective Geometry and the Klein Quadric
(Library Information Services, CUI Lahore, 2023) Ammara Rashid; CIIT/FA21-RMT-101/LHR; Prof. Dr. Sarfraz Ahmad
In this thesis, the main topic is the Klein quadric and its properties. In order to study this important geometric object, we will need to discuss the basics of projective geometry. We will see how the Klein quadric is defined by a quadratic equation in a projective space which has dimension 5. The main focus of the thesis will be to show that the Klein quadric is an important example of parameter space and in particular, it parameterizes all the lines in the projective space of dimension 3.
Analysing Some Topological Indices of the Line Graph Derived from the K-subdivision of the Wheel Graph
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Rabi Ijaz Cheema; SP21-BSM-030; Dr. Imran Zulfiqar Cheema; LHR TP 9890
Topological indices play a crucial role in the mathematical characterization of chemical structures and complex networks. In this paper, we analyze several topological indices of the line graph derived from the k-subdivision of the wheel graph Wn. The k-subdivision of a graph is obtained by replacing each edge with a path of k edges, transforming the original structure into a more intricate graph. The line graph of this k-subdivision further encodes adjacency relationships between edges, enabling a deeper structural analysis. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb in dices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, forgotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices for Analysing some topological indices of the line graph derived from the K-subdivision of the Wheel graph . These indices provide insights into the connectivity and complexity of the graph. Additionally, we analyze the behavior of these indices with respect to the parameter k and the number of vertices n in the original wheel graph. Our f indings reveal trends and relationships between k, n, and the computed indices, shedding light on the impact of k-subdivision on graph-theoretic properties. Theresults presented herein contribute to the broader study of graph invariants and their applications in mathematical chemistry, structural biology, and network theory
Analysis of Barrow Holographic Dark Energy in Five- Dimensional Modified Gravity
(Library Information Services, CUI Lahore, 2022) Warisha; FA21-RMT-043; Dr. Shamaila Rani
In this thesis, we assume FRW universe in context of ¯ve-dimensional Einstein Chern-Simons theory of gravity. The Barrow holographic dark energy density with Hubble horizon as boundary of the universe is taken into account to study cosmic evolution of the universe. We discuss some cosmological parameters such as coincidence parameter, density parame- ter, EoS parameter and deceleration parameter. Moreover, we also discuss the thermal stability in context of underlying scenario. We plot coinci- dence parameter which exhibit a DE dominated phase of the universe. We consider Barrow holographic dark energy model with both interacting and non-interacting scenario of dark components to evaluate these parameters and thermal stability. It is mentioned here that we obtain some consistent results representing accelerated expansion of the universe.
Application of Bilinear Neural Network Method to Sawada-Kotera Model
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Syeda Maryam Zahra; CIIT/SP21-BSM-013/LHR; Dr. Syed Tahir Raza Rizvi; LHR TP 9882
In this work, we use the bilinear neural network method (BNNM) for solving the (2+1)- dimensional bidirectional Sawada-Kotera (bSK) equation. This model is the extension of the famous Korteweg-de Vries (KdV) equation which represents the shallow water waves on surfaces. Firstly, we use generalized Hirota bilinear approach (gHBA) and then by us- ing BNNM, we obtain exact analytical solution. BNNM is an important step toward the integration of neural networks with classic methodologies for nonlinear partial differential equations (NLPDEs), presenting both the solution in exact form and offering powerful vi- sualization of complex phenomena. This may be a method applied to a wide range of ﬁelds such as plasma, optics, acoustics, ﬂuid dynamics, and so on. BNNM models the neural network with a tensor formula and derives the exact solutions by symbolic computation. This neural network consists of layers, with their contribution in ﬁnding the solutions using activation functions and weight matrices. This method generates new test functions and in this thesis, the test functions consist of ”3-2-1” and ”3-3-1” neural network models. Here ”3-2-1” means 3 neurons in input layer, 3 neurons in ﬁrst hidden layer and a single neuron in second hidden layer. Lump, lump with one kink, rogue wave, and breather lump soliton and periodic solution for the governing model will be obtained by BNNM with the men- tioned layer. Sev
Application of Ranking Heptagonal Neutrosophic Fuzzy Numbers to a Tansportation Problem
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Mudasir Nazar, Umer Farooq; CIIT/FA22-BSM-031/LHR, CIIT/FA22-BSM-59/LHR; Dr. Madiha Khalid; LHR TP 9924
This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli- cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever- aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini- mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac- terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
Application of Ranking Heptagonal Neutrosophic Fuzzy Numbers to Transportation Problem
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Mudasir Nazar (FA20-BSM-031 : Umer Farooq (FA20-BSM-059); Dr. Madiha Khalid; LHR TP 9923
This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
Application of Ranking Hexaagonal Neutrosophic Fuzzy Numbers to an Assignment Problem
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Usama Talib (FA20-BSM-044) : Zafar Iftikhar (FA20-BSM-054); Dr. Madiha Khalid; LHR TP 9920
This thesis introduces the concept of neutrosophic hexagonal numbers and presents a novel approach for their ranking. Neutrosophic hexagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic hexagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant role
Applications of B-spline in Fractional Partial Differential Equations
(Library Information Services, CUI Lahore, 2023) Fazeela Haider; FA21-RMT-069; Dr. Tayyaba Akram
The fractional derivatives have a significantly greater rate of resistance in the model for characterizing the history of variable and its features in a variety of dynamical systems. The fractional partial differential equation (FPDE) will be considered in the singular and nonsingular kernel. For the time direction, we will use singular kernel as well as non-singular kernel and for spatial direction, we are using exponential B-spline. In this thesis we presents a numerical methodology for a class of time-fractional reaction- diffusion equations using the exponential B-spline method.The time-fractional reaction-diffusion (TFRD) model offers broad physical views and theoretical interpretations, and its numerical approaches are important both conceptually and practically. A numerical approach for solving the TFRD model with the singular kernel as well as non-singular kernel is developed. The Caputo derivative operator as well as Caputo-Fabrizio operator is used to discretize time levels, while the exponential B- spline function is used to discretize space direction. In order to check the efficiency of the techniques, the stability analysis have been analyzed which is unconditional stabile. Several numerical examples are provided to demonstrate the proposed scheme’s feasibility and efficiency.
Baryogenesis in f(R) Theory of Gravity
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Laiba Zulfiqar (FA20-BSM-018) : Adeeba Iqbal (FA20-BSM-063); Dr. Rabia Saleem; LHR TP 9926
f (R) Theory of gravity are reviewed in the context of the so called gravitational baryoge nesis. The latter is a mechanism for generating the baryon asymmetry in the universe, and relies on the coupling between the Ricci scalar curvature R and the baryon current. Gravity Lagrangians of the form L(R) ∼ Rn, where n differs from 1 (the case of the General Rela tivity) only for tiny deviations of a few percent, are consistent with the current bounds on the observed baryon asymmetry.
Boundary Layer Flow Behavior of Viscoelastic Maxwell Model Fluid Over Thin Needle
(Library Information Services, CUI Lahorez v, 2023) Mariam Nissar; CIIT/FA21-RMT-019/LHR; Dr. Mohsan Hassan
In the current thesis, study of viscoelastic fluid flow through the Maxwell model is investigated over thin needle. The mathematical model of this problem is modeled by continuity, momentum and energy equations in the form of partial differential equations. The equations are simplified by boundary layer approximation and similarity transformations. The solution of these equations will be obtained by numerical technique. The results are displayed in the form of
Bounds on Second Hyper Zagreb Index for Four Graph Operations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Kainat AbdulJabbar (FA20-BSM-030) : RimshaRani (FA20-BSM-073); Dr. Maqsood Ahmad; LHR TP 9902
All praise and thanksgiving are due to Allah, the Most Gracious and Most Merciful, for His blessings and strength in finishing this thesis. It gives us great pleasure to extend our sincere gratitude to our supervisor, Dr. Maqsood Ahmad, for his energetic guidance and motivating demeanor, which made working on this project a breeze. Only with his leadership were my efforts successful. We would like to thank our institution and Dr. Muhammad Hussain, Head of the Mathematics Department, in particular for providing us with excellent research facilities that were necessary to achieve our objectives. We sincerely thank our cherished parents, relatives, and friends, as they have contributed much to our achievement.
Bounds on Second Hyper Zagreb Index for Four Graph Operations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Mehwish Perveen (CIIT/FA20-BSM-032/LHR, Mehwish Majeed (CIIT/FA20-BSM-051/LHR); Dr. Maqsood Ahmad; LHR TP 9904
In the field of chemical graph theory, a Topological index is a numerical value obtained through a mathematical formula involving vertex degrees, distance, spectrum, and their combination. These values are extracted from the molecular graph of a chemical com- pound and are instrumental in the QSPR/QSAR analysis. Operations on the graphs enables us to construct new and valuable molecular graphs of future chemical compounds. A fas- cinating area of inquiry in chemical graph theory is determining the closed form formulas and bounds of relevant topological indices within a specific family of graphs. Our project focuses on computing the exact formulas of the Y-index for F-sum related to tensor product, and we have included various examples to verify our findings.
Breathers, Rogue Wave and Lump Solutions For Nonlinear Partial Evolution Equation
(Library Information Services, CUI Lahore, 2022) Hasnain Abbas; CIIT/FA21-RMT-044/LHR
Solitons are wave packets or pulses that exhibit exceptional behavior by preserving their shape and speed while traveling through a medium. Their remarkable stability sets them apart from typical wave phenomena, as they resist dispersion and retain their characteris- tic features intact. Solitons emerged as a concept within ﬂuid dynamics during the 19th century, and their discovery is attributed to John Scott Russell, a Scottish engineer and scientist.In this thesis, our objective is to investigate and achieve various wave patterns and phe- nomena, including lump solitons (LS), lump 1 stripe soliton interaction solutions, lump 2 stripe soliton interaction solutions, generalized breathers(GBs), rogue waves (RW), ﬁrst order soliton solution, Y-type bifurcation soliton and second order solution, interactions between lump periodic and kink waves, periodic cross kink waves (PCKW), lumps with one kink (L1K), lumps with two kinks (L2K), periodic cross lump waves, periodic waves (PW), and multi waves (MW). To analyze these patterns, we employ ansatz transforma- tions, which allow us to explore homoclinic breathers (HB), kink cross rational solutions (KCRS), periodic cross rational solutions (PCRS), M-shaped rational solutions (MSRS), M-shaped interactions with rogue and kink waves, M-shaped interactions with periodic and kink waves, M-shaped rational solutions with one kink (MSRS 1k), and M-shaped ra- tional solutions with two kinks (MSRS 2k). Additionally, we study the dynamic behavior of our obtained solutions through the utilization of 3D, 2D, and contour plots.Key words: Sub-ODE method, nonlinear Schr¨
Chaotic Attractors and Delayed Mathematical Model Of Oncology
(Library Information Services, CUI Lahore, 2022) Shazia Batool; /SP21-RMT-010; DR. AYESHA SOHAIL
In the recent literature, the competition model of oncology is focused on can- cer. In chapter 1, we will study cancer with some basic examples and the lo- gistic growth of cancer cells. In chapter 2 we analyze the delay competition model and the stability at the equilibrium point must be observed. During this research, the competition model of oncology is used to demonstrate the interac- tions and dynamics of cancer and healthy cells. The impact of control measures on cell production and tumor control, and the competition for survival between the two populations, subject to natural and invoked constraints, such as oncol- ogy changes, and epidemiological conditions. The mathematical model helps to improve the limiting criteria, subject to the stable, asymptotically stable, and unstable cases respectively. The delayed dynamics subject to these constraints can be modeled well with the aid of delay differential equations. During this re- search, a delayed mathematical model is presented and the dynamical analysis is provided to support the hypothesis of delay in cancer cell harvesting.
Characterization of Total Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) SANIA MASOOD; CIIT/FA20-BSM-016/LHR; Dr. Imran Ahmed; LHR TP 9914
This thesis delves into the characterization and properties of regular total graphs and their chromatic numbers. A regular total graph is a unique graph structure where each vertex has the same degree, and the total graph, denoted as T(G), incorporates both the vertices and edges of a given graph G as vertices, with edges in T(G) representing adjacency or incidence relationships in G. The primary aim of this research is to elucidate the structural characteristics and chromatic properties of these regular total graphs. We consider “ordinary” graphs; that is, ﬁnite un-directed graphs with no loops or multiple edges. The total graph T(G) of a graph G is that graph whose vertex set is V(G)U E(G) and in which two vertices are adjacent if and only if they are adjacent or incident in G. A characterization of regular total graphs as well as some other properties of total graphs have been considered before. In this article we consider nonregular graphs and yield a method which enables us actually to determine whether or not they are total. Let G be an ordinary graph (ﬁnite, undirected, with no loops or multiple lines). Besides the chromatic number X(G) and line chromatic number X 0 (G), there is associated with G another positive integer X 00 (G), called the total chromatic number of G, which is the minimal number of colours required for colouring the elements (points and lines) of G such that no two elements which are either adjacent or incident have the same colour. The chromatic number, a fundamental parameter in graph theory, represents the minimum number of colors required to color the vertices of a graph such that no two adjacent vertices share the same color. This research aims to depend the understanding of how chromatic properties manifest in complete graphs and regular graphs. Regular graphs, the relationship between vertex degree and chromatic number is scrutinized, with new bounds and exact values established for speciﬁc classes of regular graphs. For complete graphs, the study reaﬃrms that the chromatic number is equal to the number of vertices, providing a clear and concise analysis of this well-known result. Closed loop cycle paths, also known as cycles, are fundamental structures in graphs where a sequence of vertices is connected by edges forming a loop with no repeats except for the starting and ending vertex. Understanding these cy- cles is crucial for various applications in computer science, network theory, and optimization problems. The thesis then explores diﬀerent types of cycles, such as Hamiltonian and Eulerian cycles, and their signiﬁcance in both directed and undirected graphs. Automorphisms and isomorphisms are fundamental concepts in graph theory, playing a crucial role in understanding the symmetry and equivalence of graph- s. Automorphisms, which are graph isomorphisms from a graph to itself, are explored in detail to understand the symmetries within a graph. Isomorphisms, which are bijections between vertex sets of two graphs that preserve adjacency, are analyzed to determine graph equivalence.
Computational aspects of SSC of Wheel Graphs
(Library Informaton Services, COMSATS University Islamaad, Lahore Campus, 2023) Rimsha Amber CIIT/FA20-BSM-058/LHR; Dr. Imran Ahmed; LHR TP 9922
Stanley-Reisner ideals encode combinatorial information about these complexes, bridg- ing combinatorial geometry and commutative algebra. Simplicial complexes, comprised of simplices, capture complex topological and combinatorial relationships, serving as founda- tional tools in numerous mathematical disciplines. Shellable complexes, a significant sub- class, allow systematic decomposition into ”shells,” revealing insights into their topological and homological properties. Studying the spanning simplicial complexes of wheel graphs elucidates the connection between graph theory and algebraic topology. Investigation into the shellability of line simplicial complexes sheds light on their combinatorial intricacies, contributing to a deeper understanding of their geometric and algebraic nature. Through these explorations, we uncover the rich interplay between combinatorial geometry, alge- braic structures, and topological properties inherent in simplicial complexes, facilitating broader comprehension and application across mathematical domains
Computing Connection Number-Based Indices for Graphs Derived from Metal Organic
(Library Information Services, CUI Lahore, 2023) Muhammad Adeel Arshad; CIIT/FA21-RMT-068/LHR; Dr. Hafiz Muhammad Afzal Siddiqui
Metal-organic networks consist of metals and organic ligands, forming their two distinctive components. In the realm of Mathematical Chemistry, metals are elements that exhibit metallic bonding and possess a propensity to readily form positive ions. Ligands, on the other hand, encompass neutral molecules or ions that attach to the central atoms or ions of metals, forming bonds. The recent surge in the significance of distance-based topological indices has led to their widespread use in exploring the structure-property relationship among molecules. Given their importance, this thesis focuses specifically on distance-based topological indices. It delves into Metal-organic Networks, examining their characteristics and properties. The thesis also involves the computation of several connection-based Zagreb indices to gain insights into the Metal-organic Networks. By emphasizing the role of distance-based topological indices, this study aims to contribute to our understanding of Metal-organic Networks and their structural features. The examination of these indices offers valuable information regarding connectivity and complexity, facilitating further research and potential applications in fields such as materials science, catalysis, and drug discovery. .
Computing Degree Based Topological Indices for Copper Iodide
(Library Information Services, CUI Lahore, 2023) Muhammad Sadiq; FA21-RMT-050; Dr. Muhammad Kamran Siddiqui
enhanced, particularly in the domain of chemical graph theory. Over the past few years, numerous researchers have been able to pursue a variety of novel avenues. A chemical graph is a named graph where the edges reflect chemical bonds between atoms and the vertices reflect the atoms of a compound. The investigation of topological indices is crucial for determining numerous physical and chemical characteristics of the under investigation molecular structures. Firstly, we focused on degree based topological indices, namely Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and coindices, hyper Zagreb index, forgotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Copper Iodide (CuI). Afterwards, we found the physical measures like heat of formation of Copper Iodide (CuI). Then, we fitted curves between different indices and corresponding heat of formation. Curve fitting was done in MATLAB through different methods based on linearity and non-linearity. The performance of the method was tested using mean squared error (MSE), the sum of squared errors (SSE) or R2. Further, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermodynamical properties of the chemical structure Copper Iodide (CuI).