Browsing by Author "Dr. Hafiz Muhammad Afzal Siddiqui"

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A Study of Connection-Based Indices of Certain Structures
(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Faiza Bibi; SP22-RMT-023; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 8729
A Study of Connection-Based Indices of Certain Structures
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.
Characterizing Localized Wave Structures in High-Dimensional Nonlinear PDEs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Bismah Nazir; Fa23-rmt-008; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 9756
This thesis investigates the extraction of solitons that arise in nonlinear dynamics, focus ing on two important models: the Stochastic Davey–Stewartson equation and the Ben jamin–Bona–Mahony (BBM) equation well known Nonlinear Evolution equation. Numer ous physical events are described by these models, which are well known for their intricacy in nonlinear wave propagation. These models are solved using the Extended Modified Aux iliary Equation Method (EMAEMM), a potent yet effective technique for resolving nonlin ear partial differential equations (NLPDEs). By simplifying the equations, the EMAEMM approach facilitates the search for precise solutions, making it a valuable tool in nonlinear analysis. Optical fibers, fluid dynamics, and plasma physics are just a few of the many applications that benefit from the soliton’s ability to maintain its shape while propagating. A variety of graphical representations, all created using Mathematica, are displayed, in cluding 2D, 3D, density linear, 1D, slice contour plotting, and stream density plots, and the stability and sensitivity of the resulting solitons are investigated. Bright, dark, kink, periodic, and optical solitons are among the many different behaviors of the reported soli tons. This thorough analysis of soliton dynamics in nonlinear systems offers insights on the stability and representation of solitons in mathematical physics
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. .
Evaluation of Connection Number-Based Indices of Networks Derived from Triglycerides
(Library Information Services, CUI Lahore, 2023) Hudaa Zaidi; FA21-RMT-036; Dr. Hafiz Muhammad Afzal Siddiqui
Graph theory serves as the fundamental framework for chemical informatics, utilizing topological indices to generate chemical structures and establish connections between real numbers and molecular graphs. In 1974, Gutman and Trinajstic introduced connection-based Zagreb indices as molecular descriptors to analyze the topological properties of chemical compounds. These indices were subsequently named Zagreb indices. Building on this research, Ali et al. further explored the applicability and properties of Zagreb indices in theoretical chemistry and molecular modeling. This thesis specifically focuses on the computation of connection-based number indices for triglycerides, as well as their line and para-line graphs. By studying these indices, the aim is to gain insights into the topological characteristics of triglyceride structures and their corresponding graph representations. This research contributes to the broader field of chemical informatics, providing valuable information for the analysis and modeling of complex molecules. .
Extraction of Solitons Emerging in Nonlinear Dynamics
(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Bismah Yousaf; SP23-RMT-006; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 9574
The extraction of solitons that emerge in nonlinear dynamics is examined in this thesis, with particular attention to two significant models: the Perturbed Chen-Lee-Liu and the Biswas Milovic models. These models, which are renowned for their complexity in nonlinear wave propagation, describe a wide range of physical phenomena. The Extended Modified Auxil iary Equation Method (EMAEMM), a powerful yet efficient method for resolving nonlinear partial differential equations (NLPDEs), is used to derive solution solutions to these mod els. The EMAEMM method is a useful tool in nonlinear analysis as it makes it easier to find exact solutions by breaking down the equations into simplified forms. The ability of soliton to hold its shape during propagation makes it useful in a variety of applications, including fluid dynamics, optical fibers, and plasma physics. The stability and sensitivity of the resulting solitons is examined, and a number of graphical representations—all gen erated via Mathematica—are shown, including 2D, 3D, density linear, 1D, slice contour plotting, and stream density plots. The observed solitons exhibit a wide variety of behav iors and include bright, dark, kink, periodic, and optical solitons. Insights into the stability and representation of solitons in mathematical physics are provided by this comprehensive examination of soliton dynamics in nonlinear systems.
Graph Neural Networks: Bridging Structure and Intelligence
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Fahad Shoaib; SP21-BSM-007; Dr. Hafiz Muhammad Afzal Siddiqui; LHT TP 9880
Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on non-Euclidean data, bridging the gap between structured graph representations and intel ligent data processing. This thesis explores the theoretical foundations and architectural innovations of GNNs, focusing on their ability to capture complex relational patterns in graph-structured data. We begin by examining the Message Passing Framework, which forms the backbone of most GNN architectures, enabling information propagation across graph nodes. The study then delves into Graph Convolution Operations, highlighting how they generalize traditional convolutions to irregular graph domains. We provide an in-depth analysis of two key GNN architectures: Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs). GCNs are presented as a foundational model that efficiently aggregates neighborhood information, while GATs are explored for their adaptive atten tion mechanisms that allow for more flexible and expressive feature learning. Through a comparative analysis, we elucidate the strengths and limitations of these architectures, with particular emphasis on citation network analysis, where nodes represent scientific papers and edges represent citations between them. Our experiments on the CORA dataset, com prising 2,708 scientific publications and 5,429 citation links, demonstrate the effectiveness of GNNs in capturing the interdependence between academic papers and their citations.
Locating and Fault-Tolerant Locating Numbers of Certain Structure.
(Library Information Services, CUI Lahore, 2022) Khadija Mazhar; SP21-RMT-022/; Dr. Hafiz Muhammad Afzal Siddiqui
A branch of mathematics called chemical graph theory unifies graph theory and chemistry. Molecules are mathematically modelled using graph theory to reveal the physical characteristics of these chemical compounds. Here chemical structure can be expressed in the form of graph. In chemical graph the vertices represent the compound's atoms, and the edges represent its chemical bonds. For a connected graph ?, a resolving set is a subset of ?(?) that is used to uniquely identify all vertices of graph by means of distance codes in such a way that all the vertices have distinct codes, if the resolving set is minimum that is called basis for ? and its cardinality termed as metric dimension or location number. If all the vertices of the graph are identified by at least one pair of vertices of resolving set, then this set is referring as fault-tolerant resolving set and if this set is minimum then its cardinality is called fault-tolerant metric dimension. This thesis comprised of five main chapters whose details are: first chapter is about introduction, second consist of literature review, chapter 3 and 4 consist of main results in which we study fault-tolerant metric dimension of chemical structure. We show that this parameter is unbounded if we consider n-unit structure. Finally, in chapter 5 we present conclusion of the thesis and some future directions.
Resolving Properties of Graphs Associated to Commutative Rings
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Ammar Mujahid; FA19-RMT-101; LHR TP 7382; Dr. Hafiz Muhammad Afzal Siddiqui
Let 𝑆 be a finite commutative unital ring having some non-zero elements 𝑥 and 𝑦 such that 𝑥𝑦=0. The elements of 𝑆 possesses such property are called the zero-divisors, the set of all these elements is denoted by 𝑍(𝑆). We can associate a graph to 𝑆 by means of a zero-divisor set 𝑍(𝑆) denoted by 𝜁(𝑆) (called the zero-divisor graph) to study the algebraic properties of the ring 𝑆. In this research work, we aim to produce some general bounds for edge and mixed version of metric dimension regarding some zero-divisor graphs of some families of rings. Then we prove general result for the upper and lower bounds of edge metric dimension of zero-divisor graphs in terms of maximum degree and diameter of 𝜁(𝑆). Finally, we discuss some relationships between girth, diameter and mixed metric dimension of zero-divisor graphs.
Secure Resolving Dimension of Zero Divisor Graphs Associated to Commutative Rings
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Muzammil; CIIT/SP20-RMT-012/LHR; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 7626
This Thesis contains the study of secure resolving dimensions of certain zero divisor graphs of commutative ring with unity. A subset 𝑇 of 𝐺 is a secure resolving set for 𝐺 if 𝑇 is resolving and for any 𝑥 ∈ 𝑉 − 𝑇, there exists 𝑦 ∈ 𝑇 such that (𝑇 − {𝑦}) ∪ {𝑥} is a resolving set for 𝐺. The minimum cardinality of a secure resolving set for 𝐺 is known as the secure resolving dimension for 𝐺. We determine the secure resolving dimension of various zero divisor graphs derived from commutative ring with unity and prove that all these graphs have constant secure resolving dimension
Use of Artificial Intelligence Approach For Visual Prediction & Transfer Learning
(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Hafiz Syed Muhammad Hur; FA22-RMT-037; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 9381
In this work, we introduce the identification of the MNIST database, which will be in handwritten digits that the machine can identify. The human handwriting form may be de tected and converted into computer language. We use several machine learning algorithms, including Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), and Bidirectional Long Short-Term Memory (BiLSTM). The MNIST database was developed using binary images of handwritten numbers (09) from NIST’s Special Database.Second, introduce the identification of TB photos. Tuber culosis is the biggest cause of mortality worldwide, according to the World Health Organi zation. Inadequate treatment and delayed or incorrect diagnosis have led to several cases of the illness. Accurate and timely diagnosis is critical for successfully managing and preventing tuberculosis. Despite significant progress in deep learning for medical image processing. There are two types of distributions: training and application data.Our findings show that transfer learning from a pre-trained vision transformer outperforms a pre-trained CNN in medical imaging
Zero Forcing Number of F-Sum of Some Families of Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Aleeha Shahid; CIIT/SP20-RMT-020/LHR; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 7651
This thesis deals with zero forcing number of 𝐹-sum of graphs derived from certain families of graph. A zero forcing set of graph 𝑆 is a set 𝑆 ⊆ 𝑉 such that there are no white vertices in the derived coloring of 𝑆. The zero forcing number of 𝐺 is 𝑍(𝐺) = min⁡{|𝑆|: 𝑆⁡is zero forcing set of⁡𝐺}. We study zero forcing number of 𝐹-sum of two path graph, two cycle graph and then path and cycle graph. It has been proved that it is constant in case of 𝑆 operation of 𝐹-sum and unbounded otherwise.