Final Year Projects (FYPs)

Now showing 1 - 3 of 3

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 9912
In 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.
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 9888
Metal–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.
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 9918
This 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.

Final Year Projects (FYPs) - Undergraduates

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