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 Fractional Metric Dimension of Different Chemical Structures(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Muhammad Junaid Rashid; FA18-RMT-055; LHR TP 6459; Dr. Imran Zulfiqar CheemaThe Metric Dimension of a graph G is the minimum number of basis element in a resolving set. Let Q= {q1, q2, q3,…, qk} is the set of vertices of G. The representation r(u/Q) of u with respect to Q is the k-tuple {d(u,q1 ), d(u,q2 ), d(u,q3 ), …, d(u,qk )}, where Q is called a resolving set [4], if every vertex of G is uniquely identified by its distances from the vertices of Q, or equivalently, if distinct vertices of G have distinct representations with respect to Q. Minimum number of vertices in a resolving set is called the basis for G and the number of basis elements is known as the metric dimension of G denoted by dim (G) [10]. In recent years some mathematics work on the concept of resolving sets and metric basis [1, 7, 13]. We have an ordered set of vertices Q ={q1, q2,…, qk } of a graph G, the d(u,qi ) is zero iff u= qi. If r(s/Q) ≠ r(t/Q) for each pair of distinct vertices s,t belongs to V(G)\Q then Q is called a resolving set. The Fractional Metric Dimension of G is defined as dim f(G) = {|g|: g is minimal Resolving function of G} Where |g| = ∑ V∈Vg (v). In the graph theory the most important research study in integer-valued graph theoretic concept of fractionalization. The research is about different chemical structure and convert these structure into planar network graphs. Consequently to calculate the fractional metric dimension of these network graphs. In this thesis, we investigated metric dimension and fractional metric dimension of Line Graph of Polythiophene Network and Backbone Network.Item Topological Indices on k-Subdivision Graphs of Cubic Zirconia Network (CZ)(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Mudassarah Tasneem; FA23-RMT-024; Dr. Imran Zulfiqar Cheema; LHR TP 9770Graph theory has gained extensive application across various dis ciplines, with chemical graph theory emerging as one of the most vibrant areas of research. Graph theoretical approaches have been used in several studies in recent years to study various chemical net works and structures. These representations use atoms as vertices and chemical bonds as edges. In order to understand the physical and chemical characteristics of molecules, this field of study focuses on investigating topological indices. In this work, we examined a number of degree-based topo logical indices, such as the Augmented Zagreb index, the First and Second Zagreb indices, the Atom Bond Connectivity (ABC) index, the Geometric Arithmetic (GA) index, and Hyper Zagreb index. For the cubic zirconia (ZrO2) network in particular, we also took into account revised Zagreb-type indices. These mathematical models could provide useful resources for investigating the cubic zirconia structure’s thermodynamic features, improving our comprehension of its physics and chemical activity.Item Computation of Some Fundamental Topological Indices for the Line Graph of M-Subdivision of Triangular Oxide Network (TOX)(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Majid Siddique; FA23-RMT-020; Dr. Imran Zulfiqar Cheema; LHR TP 9767Afascinating field of study in graph theory is the investigation of topological invariants for the line graph of m-subdivision of Triangular Oxide Network (TOX). This abstract seeks to identify basic traits that can be utilized to differentiate and categorize this structure by examining the intrinsic qualities of this line graph. To understand the complexity and con nectivity of this line graph, topological invariants such the chromatic number, girth, and connectedness are investigated. In order to reveal further structural details, algebraic invari ants like the spectrum and eigenvalues are also investigated. The findings of this study not only advance our knowledge of the Triangular Oxide Network but also have the potential to influence a number of disciplines where accurate characterization of complex systems is crucial, such as computational chemistry, materials science, and network analysis.