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 Zero Forcing Number of Optical Transpose Interconnection System Swapped Network(Library Information Services, CUI Lahore, 2023) Shamza Jabeen; SP20-RMT-040; Dr. M. Faisal Nadeemnodes is a two-level swapped architecture built by 𝑛 copies of an n-node basis network that constitutes its clusters. We explore the relations between basis network and optical transpose interconnection system (OTIS) swapped networks. We assume that the processor/nodes of the basis network are labeled [𝑛] = 1, . . . , 𝑛, and the processor or node labeled by 〈g, p〉 in OTIS network Ω identifies the node g in cluster p, and this corresponds to node 〈g, p〉 ∈ V(Ω). Subsequently, the cluster address of node 〈g, p〉 will be referred to as g, while the processor address will be referred to as 𝑝. In this thesis, our focus is on finding the zero-forcing number of OTIS swapped networks. Here, we show that the swapped connectivity actually introduces a desirable property that may not exist in the basis network. We construct OTIS swapped networks from the basis networks path, cycle, star, complete, wheel, fan and friendship and then find the zero forcing number of these OTIS swapped networks. We find new auxiliary for zero-forcing number of these graphs. We described that the zero-forcing number will be different for different graphs.Item On Entropy Measure of Different Families of Fullerenes(Library Information Services, CUI Lahore, 2023) Hafsa Iqbal; FA21-RMT-006; Dr. M. Faisal NadeemA topological index is a numerical value assigned to a graph, which represents specific topological properties or characteristics of the graph. It serves as a quantitative measure to analyze and compare the structural features of different graphs. Topological indices have extensive applications in the field of graph theory, enabling the study and understanding of various graph structures and their properties.Topological indices can be categorized based on three main criteria: degree, distance, and spectrum. These categories help organize the different types of indices and provide a framework for analyzing graph structures.Hosoya entropy is a metric in graph theory that quantifies the complexity of a graph’s struc- ture and the connectivity patterns it exhibits. It is computed using the Hosoya polynomial, which counts the number of distinct walks between any pair of vertices in the graph. The resulting Hosoya entropy value provides a numerical representation of the graph’s topolog- ical characteristics and symmetry properties. In this thesis we compute the Hosoya entropy of different fullerene graphs by understanding the structures of fullerenes and compute dis- tance to partition them in Hosoya classes.Item Roman Domination Number of Split Graphs of Certain Graphs(Library Information Services, CUI Lahore, 2022) Ghulam Mustafa; SP23-RMT-009; Dr. M. Faisal NadeemA dominating set D in a graph G = (V; E) is a subset of vertices such that every vertex not in D is adjacent to at least one vertex in D. The minimum cardinality of such a set is called the dominating number of G. A Roman dominating function on G is a function f : V ! f0; 1; 2g with the property that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function f is defined as and the minimum possible weight over all Roman dominating functions on G is called the Roman dominating number, denoted by gadjacent to every neighbor of v. In this work, we explore how different graphs relate to their corresponding split graphs SItem 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 On Some Degree Based Topological Indices of Tetracyano Benzene Metal Organic Framework(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Aqib Javaid; CIIT/SP21-BSM-028/LHR; Dr. M. Faisal Nadeem; LHR TP 9888Metal–organic frameworks (MOFs) play a pivotal role in modern materials science due to their highly porous and customizable structures, which are ideal for applications such as gas storage, catalysis, and drug delivery. To model these complex structures, chem- ical graph theory offers a powerful mathematical framework that captures the molecular architecture of MOFs. Within this framework, topological indices—also known as molec- ular descriptors—serve as mathematical formulations derived from the molecular models. These descriptors allow researchers to analyze the physicochemical properties of MOFs without resorting to expensive laboratory experiments, thus streamlining the study of struc- ture–property and structure–activity relationships in mathematical chemistry. In this project, we focus on the tetracyanobenzene-based metal–organic framework, systematically computing and examining its various molecular descriptors. A numerical comparison of these descriptors is provided, offering insights into the framework’s charac- teristics and potential applications.Item On the Bounds of the Second Fuzzy Zagreb Index in Fuzzy Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Talha Ishaq (FA20-BSM-034) : Mehrab Saeed (FA20-BSM-046); Dr. M. Faisal Nadeem; LHR TP 9918This project explores the fuzzy Zagreb topological indices within the framework of fuzzy graph theory, focusing on their applications and significance in various real-world scenar ios. Fuzzy graph theory, an extension of classical graph theory, accommodates the concepts of uncertainty and imprecision, which are inherent in many practical situations. This study begins by introducing the fundamental concepts of fuzzy sets and fuzzy graphs, as pio neered by Zadeh and Rosenfeld. In the first chapter, we discuss the basic definitions of graph theory. In the second chapter, we go through a history or literature review. In the third chapter, we have discussed the second Zagreb indices and their main results. In the fourth chapter, we have mentioned the conclusion of our project. The research then delves into the specific domain of fuzzy Zagreb indices, including both the first and second indices, and their roles in analyzing and predicting properties of fuzzy graphs. These indices provide a robust mathematical approach for handling complex systems characterized by fuzziness. The project presents detailed definitions, theorems, and proofs related to the second Zagreb index for various fuzzy graph structures, includ ing fuzzy path graphs, cycle graphs, wheel graphs, star graphs, complete bipartite graphs, complete graphs, and Petersen graphs. Asignificant portion of the study is dedicated to calculating the second Zagreb index for different fuzzy graph models, supported by illustrative examples. These examples demon strate the practical application of theoretical concepts, providing a clear understanding of how fuzzy Zagreb indices can be utilized to solve problems in fields such as chemistry, ix pharmaceutical engineering, and network analysis. Overall, this project contributes to the field of fuzzy graph theory by offering com prehensive insights into fuzzy Zagreb indices, their theoretical underpinnings, and their practical applications. The findings highlight the importance of these indices in modeling and analyzing systems where traditional crisp graph approaches are inadequate, thus paving the way for further research and development in fuzzy systems and their applications.