Department of Mathematics

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    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.
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    Resolving Topological Index Of Graphs Associated
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Ali Bahadar; FA19-RMT-109; Dr. Kashif Ali; LHR TP 7394
    In this thesis, we study a well-known concept of graph theory, called resolvability, in con- text of two types of graphs ( commuting and non-commuting) associated to two algebraic structures (dihedral and semi-dihedral groups). By analyzing the resolving share and the average resolving share of each vertex, we compute the resolving topological index of each graph.
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    Radio Labeling of Different Graphs
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) AMNA RIAZ; CIIT/FA19-RMT-057/LHR; Dr. Muhammad Hussain; LHR TP 7406
    This thesis is about Radio Labeling. For a graph G, any two vertices, v1 and v2 in G, Let d(v1, v2) represent the distance between v1 and v2. Let diameter of G is diam(G). A Multi-level distance labeling(radio labeling) for G is a function f that assign to each vertex so that they can satisfy this condition d(v1, v2) + |f(v1) − f(v2)| ≥ diam(G) + 1 The main purpose for this research is to find the radio number of Web graph rn(Wn), embedded graph rn(Emn) and radio number of double wheel graph rn(DWn). we use basic concept to find their radio numbers.
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    On Topological Study Of Face Cubic Lattice FCC(N)
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Anum Shahzadi; FA19-RMT-062; Dr. Hani Shaker; LHR TP 7385
    This study explores the topological properties of the Face-Centered Cubic (FCC) lattice, denoted as FCC(N), which is widely used to model crystalline structures in solid-state physics and materials science. The research focuses on analyzing the structural arrangement, connectivity, and symmetry of the FCC lattice using concepts from graph theory and topology. Key properties such as vertex coordination, edge relationships, and lattice transformations are examined to understand how the topology influences physical characteristics like stability, density, and atomic interactions. The findings highlight the mathematical significance of FCC(N) and its applications in modeling complex three-dimensional networks.
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    On Some Combinatorial Properties Of Graphs, Posets
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Muhammad Arfan Ali; FA12-PMATH-002; Dr. Sarfarz Ahmad; LHR TP 5945
    This work investigates fundamental combinatorial properties of graphs and partially ordered sets (posets), focusing on structural relationships, ordering principles, and enumeration techniques. Concepts from Graph Theory and Order Theory are used to analyze connectivity, comparability, chains, antichains, and lattice structures. The study highlights how these discrete frameworks can be applied to solve problems in optimization, data organization, and theoretical computer science. Emphasis is placed on key invariants and combinatorial methods that reveal deeper insights into the organization and behavior of discrete systems.
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    Machine Learning and Graph Theory towards Prediction of Drugs and Diseases
    (Library Information Services COMSATS University Lahore Campus, 2024-03-17) Naila; FA22-RMT-035; Dr.Sana Javed; LHR TP 9351
    This thesis investigates the use of machine learning approaches to predict and analyze drug properties in terms of topological indices, which are important for understanding their chemical and biological characteristics. Topological indices, generated from graphical rep resentation of chemical formation of drugs, give a measurable assessment of the molecule’s structure and are widely utilized in drug design and discovery. Firstly, we compute the topo logical indices of various cancerous drugs including Randic, Zagreb, Nirmala, geometric quadratic and quadratic geometric indices. Afterwards, we find the physical measures like molecular weight of these drugs. Then, we conduct the correlation analysis to capture the relationship between each pair of attributes in the data. Especially, to see the linear re lationship between molecular weight and indices. Firstly, we develop different machine learning models to check which fits the best. The performance of the model is tested using mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE) and the sum of squared errors (R 2 ). Mainly, we have focused on (R 2 ). Further, we show graphical representation of few of these models. This study uses advanced machine learn ing methods to improve the accuracy and efficiency of predicting the drug property namely molecular weight, allowing for faster screening and optimization of medication candidates. These findings might be helpful for investigating cancerous drugs used in the thesis based on topological indices at a deeper level.Machine Learning