Department of Mathematics

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Author: search.filters.author.Dr. Muhammad Kamran SiddiquiSubject: search.filters.subject.Topological Indices

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    Reverse Degree Based Topological Indices of Chemical Graphs
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Tayyab Younas; CIIT/FA19-RMT-064/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 7428
    Graph theory is playing a key role in applied and pure mathematics. The scope of graph theory is expanding day by day. In this thesis, we have evaluated some reverse degree based topological indices, namely, the reverse general Randic index for ∝= 1, −1, 1 2 , − 1 2 , the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse first and second Zagreb indices, the reverse first and second Zagreb co-indices, the reverse forgotten index, the reverse hyper Zagreb index, the reverse Balaban index, the reverse first and second multiple Zagreb indices, the reverse redefined first, second and third Zagreb indices for some chemical and lattices graphs like as Remdesivir, transition metal tetra cyano benzene organic network (𝑇𝑀 − 𝑇𝐶𝑁𝐵),metal organic superlattice and trans-Pd-(𝑁𝐻2)S lattice. My thesis comprising of five chapters. In the first chapter we will define some fundamental definitions. In the 2nd chapter, we will find reverse degree based topological indices for Remdesivir and transition metal tetra cyano benzene organic network (𝑇𝑀 − 𝑇𝐶𝑁𝐵). In the 3rd chapter, we will find reverse degree based topological indices for metal organic superlattice and trans-Pd-(𝑁𝐻2)S lattice. In the 4th chapter, we will present the conclusion of our thesis. In the 5th chapter, we will present the references of our thesis.
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    Exploring Topological Indices for Magnesium Nitrogen via Curve Fitting Model
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Nida Ahsan (FA23-RMT-046); Dr. Muhammad Kamran Siddiqui; LHR TP 9789
    The use of graph theory in many fields of study has increased significantly, especially in the field of chemical graph theory. Many scholars have been able to explore a range of new directions in the last few years. A chemical graph is a named graph in which the atoms of a compound are represented at the vertices, and the edges represent chemical bonds between atoms. Determining various physical and chemical properties of the molecular structures under study requires an examination of topological indices. Firstly, we focused on degree-based topological indices, namely the Randic´ index, atom bond connectivity in- dex, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, for- gotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Magnesium Nitrogen MgN4. Afterward, we found the physical measures like the heat of formation of Magnesium Nitrogen MgN4. Then, we fitted curves between different indices and the corresponding heat of formation. Curve fitting was done in MATLAB through different methods based on linearity and non-linearity. The performance of the method was tested using mean squared error (MSE), the sum of squared errors (SSE) or R2. Fur- ther, we gave graphical representations of these indices. These mathematical frameworks might provide a way to study the thermo dynamical properties of the chemical structure Magnesium Nitrogen MgN4
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    On Topological Indices of Molecular Graph of Icosahedral Nanosheet
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Seerat; CIIT/SP21-BSM-032/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 9892
    The utilization of graph theory in multiple branches of research has been vastly enhanced, particularly in the domain of chemical graph theory. Over the past few years, numerous re- searchers have been able to pursue a variety of novel avenues. A chemical graph is a named graph where the edges reflect chemical bonds between atoms and the vertices reflect the atoms of a compound. The investigation of topological indices is crucial for determining numerous physical and chemical characteristics of the under-investigation molecular struc- tures. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, forgotten index, augm,ented Zagreb index, Balaban index, redefined Zagreb type indices, of Molecular ,Graph of Icosahedral Nanosheet.
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    On Topological Indices of Molecular Graph of Bismuth Iodide
    (2024) Maira Alam CIIT/FA20-BSM-020/LHR Momina Khalil CIIT/FA20-BSM-072/LHR; Dr. Muhammad Kamran Siddiqui; LHR TP 9897
    The utilization of graph theory in multiple branches of research has been vastly enhanced, particularly in the domain of chemical graph theory. Over the past few years, numerous re- searchers have been able to pursue a variety of novel avenues. A chemical graph is a named graph where the edges reflect chemical bonds between atoms and the vertices reflect the atoms of a compound. The investigation of topological indices is crucial for determining numerous physical and chemical characteristics of the under-investigation molecular struc- tures. Firstly, we focused on degree-based topological indices, namely the Randic index, atom bond connectivity index, geometric arithmetic index, the first and the second Zagreb indices and co-indices, the first and the second multiple Zagreb indices and co-indices, hyper Zagreb index, forgotten index, augmented Zagreb index, Balaban index, redefined Zagreb type indices, of Molecular Graph of Bismuth(|||) Iodide.