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.
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Item 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 9924This 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 roleItem Deviation of Rotating Black Hole in Loop Quantum Gravity from Kerr Black Hole(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) MADIHA KANWAL; CIIT/FA20-BSM-041/LHR; Dr. Muhammad Zubair; LHR TP 9916First and foremost, I would like to thank ALLAH Almighty (the most beneficent and most merciful) for giving me the strength, knowledge, ability and opportunity to undertake this research study and to preserve and complete it satisfactorily. My heartiest gratitude to Hazrat Muhammad (S.A.W) for His guidance to humanity and for material and spiritual uplift. I would like to express my deepest gratitude to my supervisor Dr. Muhammad Zubair, for his excellent guidance, interest, patience, and for providing me a decent atmo- sphere for the research. It was not an easy task but his extraordinary support made it so. I am also thankful to my senior research fellow Muhammad Ali Raza (PhD student) who always taught me with his humble attitude and with whom I collaborated and learned many things. Lastly, I would like to thank my parents and siblings, who always supported me and prayed for my success. Without their support, love and efforts, I would have not achieved all this. They gave me wings to fly.Item Properties of Total Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) BISMA ATIQ; CIIT/FA20-BSM-007/LHR; Dr. Imran Ahmed; LHR TP 9913With every graph G (finite and undirected with no loops or multiple lines) there is associated a graph L(G), called the line-graph of G, whose points correspond in a one-to-one manner with the lines of G in such a way that two points of L(G) are adjacent if and only if the corresponding lines of G are adjacent. Let G = (V, E) be a graph. The Gallai total graph ΓT (G) of G is the graph, where V (ΓT (G)) = V ∪ E and uv ∈ E(ΓT (G)) if and only if (i) u and v are adjacent vertices in G, or (ii) u is incident to v or v is incident to u in G, or (iii) u and v are adjacent edges in G which do not span a triangle in G. The anti-Gallai total graph ∆T (G) of G is the graph, where V (∆T (G)) = V ∪ E and uv ∈ E(∆T (G)) if and only if (i) u and v are adjacent vertices in G, or (ii) u is incident to v or v is incident to u in G, or (iii) u and v are adjacent edges in G and lie on a same triangle in G. The Gallai middle graph ΓM(G) of a graph G = (V, E) is the graph whose vertex set is V ∪E and two edges ei, ej ∈ E are adjacent in ΓM(G), if they are adjacent edges of G and do not lie on a same triangle in G, or if e = uv ∈ E then e is adjacent to u and v in ΓM(G). The anti-Gallai middle graph ∆M(G) of G is the graph whose vertex set is V ∪E and two edges ei, ej ∈ E are adjacent in ∆M(G) if they are adjacent in G and lie on a same triangle in G, or if e = uv ∈ E then e is adjacent to u and v in ∆M(G).In this paper, we present Eulerian and Hamiltonian properties of Gallai and anti-Gallai middle graphs. In this paper, we investigate Total Graph, Gallai and anti-Gallai Total Graphs and Middle graph.Item 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 9904In 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.Item On Equitable Coloring of Certain Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Ahmed Muhammad (CIIT/FA20-BSM-022/LHR), Sohail Abu Haraira (CIIT/SP20-BSM-013/LHR); Dr. M. Faisal Nadeem; LHR TP 9912In this project, we explore several fundamental concepts in graph theory, focusing primarily equitable edge coloring. An equitable edge coloring of a graph is a proper edge coloring for which the difference between any two color classes is at most one. The minimum cardinality of G for such coloring is called equitable edge chromatic number.Item Study of fractional nonlinear Schr¨odinger equation for soliton solutions(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Azrar-Ul-Hassan (CIIT/FA20-BSM-036/LHR), M. Raheel (CIIT/FA20-BSM-045/LHR); Dr. Syed Tahir Raza Rizvi; LHR TP 9905The fact that nonlinear partial differential equations (NLPDEs) are used in practically ev- ery academic domain including biology, chemistry, physics, mechanics, fiber optics, at- mospheric science, and electronics research makes them significant. One special kind of NLPDE is the nonlinear Schr¨odinger equation (NLSE), research in the fields of engineer- ing, biology, and physics has uses for the NLSE. A major subject of nonlinear model re- search during the past 20 years has been the soliton, an essential description in the NLSE analysis. Particularly, the development of optical solitons has given nonlinear optics a the- oretical foundation. In the framework of the time-fractional cubic-quintic nonlinear Schr¨odinger equation (TFCQ- NLSE), the analysis of soliton solutions is the main emphasis of this work. Wide-ranging applications of this adaptive model can be found in many complicated real phenomena, such as fiber optic communication, nonlinear optics, optical signal processing, laser-tissue interaction in medical science, and many others. The intensity of the cubic and quintic non- linear components determines the observed nonlinear effects, which include self-focusing, self-phase modulation, and wave-mixing. This model’s investigation employs a robust analytical approach. Our sub-ode approach, will be multitude of potential solitons and furnishes details on the interactions of laser pulses, was employed to explore this model. This inquiry yields numerous illustrated soliton solutions. Among these solutions are those that are hyperbolic, rational, singular, bright, Jacobian elliptic solutions (JES), Weierstrass elliptic solutions (WES) and periodic solutions (PS)Item explores the application of observational data to constrain gravi- tational models(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Rizwan; CIIT/FA20/BSM-056/LHR; LHR TP 9921This thesis explores the application of observational data to constrain gravi- tational models within the framework of f(G, T ) gravity, focusing on cosmol- ogy. Three distinct models were investigated: f(G, T ) = βGn + γT , f(G, T ) = βG + ηemT , and f(G, T ) = βGn + λ √ −T . Using Python-based analysis, the Hubble parameter H(z) functions were derived from these models by applying the gravity equations and the equation of state (EoS). Key cosmographic pa- rameters, including the deceleration parameter q(z), jerk parameter j(z), snap parameter s(z), and lerk parameter l(z), were calculated and analyzed. By gen- erating plots of H(z) and the cosmographic parameters for various values of the constants (β, γ, η, λ), the sensitivity of the models to these parameters was assessed. The results highlight the significance of accurately selecting these con- stants to describe the universe expansion dynamics, demonstrating the impor- tance of observational data in constraining gravitational models.Item 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 9914This 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.Item House Price Prediction by using Machine Learning(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Laiba Faisal (CIIT/FA20-BSM-057/LHR), Ameema Umar (CIIT/FA20-BSM-053/LHR); Dr. Hani Shaker; LHR TP 9909The goal of this project is to create a machine learning model that can predict home selling prices by taking into account variables like location, square footage, number of bedrooms and bathrooms, and other relevant characteristics. The model prioritizes optimization for managing missing data in order to produce trustworthy estimates for the real estate market. This study advances real estate predictive modelling by using rigorous analysis and experimentation. It provides practitioners and stakeholders with useful information for making precise cost projections.Item Connectivity of Total Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Rimsha Imran; CIIT/FA20-BSM-033/LHR; Dr. Imran Ahmed; LHR TP 9915We associate with a graph (finite, undirected, without loops and multiple lines) a graph T(G), called the total graph of G. This new graph has the prop- erty that a one-to-one correspondence can be established between its points and the elements (points and lines) of G such that two points of T(G) are adjacent if and only if the corresponding elements of G are adjacent or incident. Connectivity is a basic concept of graph theory. It defines whether a graph is connected or disconnected. Without connectivity, it is not possible to traverse a graph from one vertex to another vertex. A graph is said to be connected graph if there is a path between every pair of vertex. From every vertex to any other vertex there must be some path to traverse. This is called the connectivity of a graph. In graph theory, an automorphism of a graph G is a permutation of the vertices that preserves the adjacency structure of the graph. In simpler terms, it’s a re-labeling of the vertices such that the overall shape or structure of the graph remains unchanged. Formally, let G=(V,E) be a graph with vertex set V and edge set E. An automorphism of G is a bijective function f:V → V such that for any two vertices u,v in V ,u is adjacent to v if and only if f(u) is adjacent to f(v).