M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Derivation of New Class of Topological Indices Through M-Polynomial(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Arooj Asghar; CIIT/SP24-RMT-009/LHR; Dr. Maqsood Ahmad; LHR TP 10071A topological index (TI) is a numeral quantity computed from the molecule’s graphical model that provides insight into the physical, chemical, bioactive, and structural properties of the associated compound. Chemical graph theory (CGT) is the bridge between graph theory and mathematical chemistry, widely employs this tool to design and analyze existing and new compounds through QSPR/QSAR analyses. The M-Polynomial is a general ex- pression possessing abundant facts about myriad degree-related TIs. Recently, the class of K-Banhatti indices and some famous indices have been extracted from the M-Polynomial. The line graphs of the synthetic denture base polymers, namely bakelite BLst , vulcanite VUst , and polymethyl methacrylate PMst , are novel, intriguing and complex structures. In this work, initially, we aim to calculate the M-Polynomials of the above-described graphs. Using M-Polynomials, we extract several TIs such as the first and second simple, hyper, and modified K-Banhatti indices, respectively. Also, we derive harmonic K-Banhatti , GA, and ABC indices from M-Polynomials of graphs under study. Lastly, we examine the relation among the paraline graphs of bakelite BLst , vulcanite VUst , and polymethyl methacrylate PMst by comparing the computed TIs.Item Computational Approaches to Connection Number-Based Indices in Metal-Organic Graphs(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Abu Harera; CIIT/SP24-RMT-005/LHR; Dr. M. Afzal Siddique; LHR TP 10068Connection number–based topological indices play an important role in chemical graph theory by providing quantitative measures of structural characteristics in molecular and network-based systems. This thesis presents a comprehensive computational study of sev- eral connection number–based indices for metal–organic graphs and their associated line and praline´ graphs. Metal–organic networks are modeled as finite, simple, and connected graphs. For these graphs and their transformations, explicit computational expressions are developed for key connection number–based indices, including the first connection number index, second connection number index, connection number Zagreb indices, modified connection number indices, and selected degree–connection hybrid indices. Closed-form formulas are obtained in terms of fundamental graph parameters such as vertex degrees, connection numbers, and the number of edges. The effect of graph operations, particularly line graph and para line graph constructions, on the behavior of these indices is analyzed in detail. A comparative investigation high- lights how these transformations influence connectivity patterns and structural complex- ity in metal–organic graphs. The results indicate that connection number–based indices are effective in distinguishing structural variations and capturing topological properties of metal–organic networks. The findings of this thesis contribute to the theoretical advancement of connection num- ber–based topological indices and provide useful computational tools for the analysis and modeling of metal–organic structures in mathematical chemistry and related disciplines.